A lot of this can depend on the details of your situation, finances, skill set, time frame, location, etc.

If someone is a Hardware Engineer with a serious soldering station, even the issue with electrolytic capacitors might not be that big a deal; if there are no other problems with a motherboard, the electrolytic capacitors can be replaced. But try it with an ordinary
simple soldering iron and at the very least, the amount of "copper" in the motherboard itself these days will tend to function as too much of a heat sink, not let the simple soldering iron generate enough heat to remove the old solder from the damaged electrolytic capacitor, so it can be replaced with a working component.

There are various types of local repair shops these days, in some places. That might even be one of the few positive offsets from the loss of so called "computer shows" that possibly should have been called computer flea markets, or computer "fests", much like ham "fests", as well as the loss of REAL electronics stores that were freely open to the public, at least in the area where I live.

Some places specialize in selling computers but also repair them, or upgrade them. Some places repair a variety of electronics. Heck, in the area which I live, even some locations of "BatteriesPlus" a place which primarily specializes in selling batteries and related items, for example, bulbs, will repair some electronics nowadays.

Other folks have mentioned some of the possible "alternate" ways of approaching places that repair things.

If you are not fully familiar with freecycle.org it is a website through which people can "recycle" things they would otherwise throw in the trash. HOWEVER, there are a number of times when someone has upgraded something and they are getting rid of something that works; television sets is probably a good example. Although individual components such as Motherboards or single CPU's aren't necessarily the usual thing, a "WANTED" notice can be posted indicating that you have a need for something, that you want something, and you might be surprised what you can get for free, if someone who uses that organization, becomes aware that you want a specific item. In fact, on freecycle.org it is forbidden to ask for money for an item.

I replaced bulging capacitors in a monitor once - without professional equipment, just a horrible old soldering gun. Succeeded too, still proud of that. Monitor still works. But a motherboard...

Interesting.
I might also add that many countries have "Recyclicg Centers", often operating quasi-commercial shops where they re-sell all sorts of "stuff" (i.e. trash other people brought in) pretty cheap (I for one am willing to pay a little for this laudable concept). Often you can also go in the back and ask the guys working there for spare parts.

Using guidance from badcaps.net, I've revived LCDs, power supplies and motherboards a bunch of times, probably >85% of the time with LCDs, >60% with motherboards and power supplies. Highest success has been with wallwarts, 100%, but I've also done distribution amps, DVD players and more with >2/3 success. I did spend >$100 for a decent soldering station. RoHS solder is a pain to remove from motherboards.

Used motherboards I haven't often bought, maybe only thrice, and did get a DOA once promptly replaced. More often I've gotten used for free, or bought refurbs, and had 100% OK from the refurbs short term, not as good long term, a result of which I won't buy ASRock again.

2/3 of the CPUs I've bought in recent years have been used, with near 0 problems. One had thermal paste where it didn't belong, but I managed to clean it well enough to work after a couple of tries.

Interesting...and you usually succeed with these computers built from used parts? On used laptops (my computers for the last five years), my results are decidedly mixed: they work, but they always break down within a year. (Why have I kept buying them? Because it's cheap and easy. I've gotten tired of the breakdowns, though; that is why I'm reverting to a desktop.)

I briefly looked into used motherboard prices, and from the results, I'm not sure I would save much money anyway. The used versions of my new board cost somewhat less but don't offer a particularly great discount.

What I do save on is used CPUs, if they're old. Enormous savings. The CPU I bought new from Newegg was an AMD Athlon II X2 220; I paid $40 for it. I damaged that CPU (bent too many pins) and had to buy a replacement. I went used for that, but I chose a similar but faster CPU, the Athlon X2 280. Would you like to know how much I paid for it? About eight dollars. Eight dollars? I can buy two or three spares for that sort of money.

Well, this is sort of ironic: buying a brand-new motherboard carries its own risks. Because I eliminated every other possibility I could think of for why my monitor won't receive a signal from my new computer, I suspect (without proof) that the motherboard is bad, so I arranged to send it back. A possibly defective board would be unremarkable, but for the irony of discovering it while expressing skepticism about used boards.

The typical pro's for a new would be warranty and new features. It has been quite a long time since any product is tested at the end of the assembly line. Only the highest end systems will get full factory testing anymore.

Companies usually use the consumer as the final test station.

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In my younger days I spent a whole two weeks working on a piece of equipment trying to figure out why it wouldn't work after replacing a new part. Kept saying to myself "It can't be that it's a brand-new part". Yep it was a brand-new part, a bad brand-new part! Lol

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Yes.
I guess they need to be tested before one starts to use them.

That sounds like a very unfortunate statistic; in my experience laptops don't break down more than desktops. In fact neither do.
It's likely that there's something on your end causing this. Maybe bad purchase choices?

When I re-built my current desktop the (new) motherboard was one of the cheapest parts, esp. considering its central role.

yeah, see what Mike Walsh wrote about that.

There's a lot of hype around everything "Bigger, Faster, Stronger, Louder" - not only in consumer electronics.
It's madness.
Sanity is to pick up last year's big toys after the big boys dropped them.
But sanity is also to never buy the cheapest, but the second cheapest at least. And don't believe an offer that is too good to be true.

I can't even recall... I'll say +5yrs. I started with inexpensive board, CPU, etc and TV cards building an OTA DVR. When I was happy that it would work, I spend a bit more power and haven't had a major issue. Did go through a power supply, swapped cases, upgraded to another used HD.

It's retired from OTA, but use it for online streaming.... with a second generation i5 !?!?!? i5-2405S - 2.5GHz It's specifically a low power CPU, on 24x7 and by today's standard way outdated.

It plays video streamed from the internet flawlessly via browser (to avoid proprietary devices). I do have a tablo OTA DVR and use 3rd party apps to offload the recordings to the pc - it plays HD video without hesitation. HDMI to the TV, nice 60" monitor.

I can't remember how much I've spent on it all - an Intel DH77EB mother board, 8GB RAM, CPU, 32GB SanDisk SSD U110 system drive and a WD Green 3TB for mass storage.

My Dell E6510 is really old - used from ebay, still functional. I run debian stable on that for taking care of my personal and home "business".