Psu is something i dont like to take chances on.. What you have looks one of them tier 5 "no name" psu.. And if its even as half as old as mine was before it started acting weird.. Mate in all honesty if you get everything replaced and get a completely new rig..its just not worth messing up with this one. Also check this list.. Id recommend you to check the psus on tier 3 of this list. Those should be more than good enough and budget friendly.http://www.tomshardware.co.uk/forum/id-2547993/psu-tier-list.html
As for case.. It doesnt really matter much.. Its a matter of personal prefference if you like your case and intend to keep it then by all means do so. Atx mobo will fit in your atx or any other atx.