You're right that a standard ATX PSU will do (see click here for confirmation), but you don't need a fancy one costing £80+.
This Corsair click here for a lot less (i.e. £35) will do the job very nicely (I can also suggest cheaper alternatives if required).
The only thing I cannot tell you for sure is whether a PSU replacement will cure the symptoms you're experiencing. So, if possible, try to borrow a working PSU (minimum 300W) from someone to test with to confirm one way or the other. G