I'd either test or replace the CMOS battery, however, there is ABSOLUTELY NO WAY that you can adequately run that 8 core FX 8350 on ANY 760 chipset motherboard and not have major/serious problems. It will never happen. You need at the LEAST a 970 chipset board, and a good one, and preferably some flavor of 990/990fx chipset, to have much chance of running that CPU without problems. I've never seen anybody that was able to run an 8 core FX CPU on any 760 chipset board and not experience serious VRM thermal throttling. Ever.
Also, it's pretty doubtful that any 300w power supply out there is going to be enough to adequately power that system. Especially if it's going to see any kind of decent load at all. That CPU can hit 239w usage on it's own at full TDP/100% load, and then you have potentially up to 75w (Likely 65w for that GX card), plus memory, motherboard overhead, fans, drives and loss from likely being a fairly inefficient unit unless you are the rare individual with an exemplary Delta or Seasonic 300w unit. Most of the 300w range type units are generally OEM type power supplies and are not terrific quality usually. There are exceptions, but I wouldn't count on it.
These things probably all add up to WHY that system got retired to "old PC" status in the first place. It certainly doesn't make for a solid server platform of any kind.
So, now you are aware of those things, if you feel like you are STILL going to attempt to make it work, I'd test the CMOS batter to ensure there is 3v or higher in it still, which there probably isn't given the age of the platform. If there is, great, if not, replace it. If you replace it with a known good CMOS battery OR it tests good, and you still have the same problem, then the chances are pretty good that you either have a board that was burned out because it was never up to the task of handling that CPU in the first place, or a too weak or faulty power supply. You'd probably need to make certain you have dealt with those issues before attempts to go any further or determine if there is some other problem would bear any fruit at all.
The fact that you can't even get into the BIOS tells me that either you are replacing it (IF in fact you HAVE replaced it) with similarly old batteries that are no better than the original, OR the board is simply faulty. Obviously there are always exceptions so try disconnecting ALL drives, WITH a known good 3v or higher CR2032 CMOS battery, AND only a single DIMM installed (Try each slot if necessary, one at a time, being sure to turn the power off between slot changes), and if you still can't even access the BIOS then you're probably out of luck and have a dead motherboard.
IMO that is probably the case anyhow from it being run with a CPU that it never should have been run with in the first place.
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