Considering the Local Tech Shops charge $50 to do less than I just did,
that route seems not to be the most financially sound route.
If you're not a skilled tech, once you get past the basic stuff, it may require a qualified technician's time to diagnose a deeper problem to determine whether or not the problem can, in fact, be repaired. Their time and skill are what they have to sell to earn their living.
However, as we discussed, it does set limits on how much you should spend. As in this case, the answer may be that it's less expsenive to replace it than attempt to repair it.
Looks like I got a lot of good parts unless I find another MB somewhere.
Very possible. The good news is, you're at least 2/3 of the way to that machine with the parts you have.
The better news is, you showed up on one of the best and friendliest forums on the planet for good info about the parts you have and help selecting the rest of what you need to make the most of what you have.
To help others help you, make sure you have the model number of your I5 (LGA1155) and the speed of your DDR3 RAM (DDR3 1333 MHz). For example, here are the
specs for Shuttle SH61, Rev. 4.
That 250 watt PSU really isn't strong enough for your components. In fact, you may want to test your system with a known good, stronger PSU - at least 450 watts. If it's failing under load, it may still have tested OK with a simple teste while failing under the actual load presented by your systerm.
If your machine included a copy of Windows licensed specifically for your machine, you will still need a new copy of Windows because the license won't transfer to another installation. If it's retail copy, you'll be OK, and a generic OEM copy will probably work on another motherboard.
On the bright side of the down side, if you need a new copy of Windows, at least you'll have a good reason to do a clean installation of Windows 10.