Check your CPU temp, and PSU power rails.
You can do this in the BIOS.
As mentioned, it may be a good idea to check if the CPU heatsink is
correctly mounted.
It is possible that the replacement PSU is faulty tho unlikely. All power
voltages should be stable and within 5%. Some motherboards do not use all
PSU voltages.
Check all cables into the motherboard are firmnly seated. Perhaps pull them
out one at a time and plug them back in again. On accasion oxidation on plug
connectors can cause marginal connections with effects as you describe - not
common.
If the heatsink is cool to touch *and* the BIOS reports low temps then leave
the CPU heatsink alone - unless you really do want to make sure it is 100%.
A "hole" in the termal paste can cause a CPU hot spot which can cause
crashes. If the heatsink is cool to touch and the BIOS reports medium to
high temps then the heatsink is possibly not mounted correctly.
Check the ariflow through the case while you are at it. Try running the
system with the top / side off the case and note if the rate of crashes
drops ==> heat. If the CPU temp in the BIOS were previously high and is now
much better then you appear to have an air circulation issue. Make sure the
heatsink is free of gunk too - but never use a vacuum cleaner to clean them.
Remove the heatsink, clean it and mount it anew if it is clogged up.
If you remove the CPU heatsink you will need to remount it correctly. People
often do this wrong - they sometimes put the CPU heatsink on reverse of how
it should be.
You *must* use either thermal paste or a new thermal pad and clean off the
old CPU gunk if there is any. Use isopropyl alcohol for this (do not use
ether, ethyl alcohol or any other organic solvent that may disolve plastics
in or near the CPU if you use too much). Isopropyl alcohol is the standard
for cleaning such things.
It is very important particularly on hot CPU's to apply CPU thermal paste
evenly. See
www.arcticsilver.com for details on how to do this (you don't
have to use arctic silver...). Make sure you read the notes carefully for
your type of CPU and for thermal paste like what you have or get. The more
recent AS compounds are applied as a large blob whereas the older thinner
compounds must be spread evenly and thinly in a near transparent manner.