That motherboard is worth less than $10 now and it has the old faulty type capacitors on it. A wonder they've not blown yet, or maybe a couple have but not bad enough you've noticed.
First check the capacitors, make sure you have no bad ones on it.
google "capacitor plague wiki" and also "bad caps".
In AMD chips that's comparable to the older socket "A", to give an idea how long past it's prime is.
Almost any CPU you get now would be used and off Ebay. They are also 10 years old or older.
Here's info on the CPU's for that motherboard
I have an old desktop with a Gigabyte 8I845PE-RZ motherboard. I want to know what would be the best CPU and GPU for this computer. I have done some research and for CPU - Celeron D335 or Intel Pentium 4 3.4ghz. As for GPU HD3850 or 7600gs.