I have a Lenovo ThinkCentre M710s with an old Linux distro on it and Windows wiped out but no wifi access.

Is it a reasonable expectation to buy a new mobo and reuse other components, including the case itself, to make a new desktop with wifi access?

Rightly or wrongly, I assume that a new mobo will be free of proprietary restrictions many computer manufacturers put in machines that are brand new.
About 15 years ago I made my own ATX box but things have changed a lot since.

Perhaps one may even suggest such mobo.

Thank you for your help.

It's common for name-brand "mid"-towers and some desktop FFs to accept standard mATX motherboards, but it's not something you can count on. For a while there was a BTX form factor that rearranged the power supply to the bottom of the tower, moving the motherboard up in the tower. That meant cables ran differently within the case. In any event, an mATX board may fit, but very likely some or all the OEM PSU's cables will end up too short, forcing you to replace board and PSU, besides CPU and RAM. Furthermore, the power switch from the case is probably within a single connector along with LED wiring that will have to be re-engineered, and wires traced to know which goes where, if they reach, instead of being labeled like on generic cases. Likely the M710 has no reset button, unlike generic cases worth having. Measure the board in the M710 now. If it matches or is slightly smaller than a board you'd like to buy, odds are it and its backpane will both fit right into the case. Cabling of OEM PSU is what's most iffy, no matter if buying new anyway. Whether the M710 has a non-standard PSU form factor is another question. Sometimes they aren't ATX, making shopping for a replacement more burdensome.

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I suggest either buying a new (or pre used) computer upgrade, or fit a wifi to your present one.

(Internal card, or external USB wifi stick.)

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rblampain,

Why do you need a new motherboard?

Unless I am missing something, all you need to do is fit either a suitable internal wifi card or a plug-in USB wifi dongle to the Lenovo M710s.

Existing motherboard looks like this:
https://www.ebay.com/itm/384046961744

The short M.2 slot on that motherboard was probably provided for the express purpose of hosting a wifi card.

Exactly.

IBM M57 wifi setup for long distance receiving on my motorcycle shop building.

https://ibb.co/VVjNTx3
https://ibb.co/XZL8Zqd

Which is a lot older than your box. IDE drive computer. I pick up all kinds of signals with that setup
The baking soda was for sand blasting that day.

It looks like that board has a long pcie slot for the GPU and 2 pcie x2 slots that would work great for a wifi card. No need to replace anything unless you just want to. Add the wifi and upgrade linux. All done and functional.