I just installed RH 7.3 on my Dell Poweredge 1750. The install did not find or configure the existing Broadcom Netxtreme BCM5704 Gigabit network controllers. What can I do to resolve this problem?

If you actually mean the Red Hat 7.3 from 2002...which is THIRTEEN YEARS AGO, why are you surprised? That hardware wasn't INVENTED when RH 7.3 was written. Load a current version...if you want to stay in the Red Hat ecosystem, then load the latest version of Fedora, and chances are it'll work.

But the latest Red Hat ENTERPRISE release is 7.0, not 7.3...and that is a commercial, PAY FOR distribution, designed for servers. Servers typically do not have things like sound, wifi, bluetooth, or even graphics and keyboards sometimes. They are designed to sit in a back room, and distros like RHEL and CentOS are poor choices for laptops or consumer hardware.

Which do you have?

RH7.3 from May 2002

it is almost as old as XP

and back in 2003 redhat basically killed off the antique Operating systems using the VERY insecure 2.4 kernel

there was a nasty bug
that the linux 2.6 kernel fixed

redhat then re-released RH9 ( younger than RH7) as Redhat ENTERPRISE linux 2.0

then
RHEL3
RHEL4
RHEL5
RHEL6
and now here we are in 2015
RHEL7


a long unsupported operating system from 2002 will not support any new hardware