How to see if mobo or CPU is dead

I Have a computer that is random **** thrown toghther and works pretty good, but it had a mobo and cpu that are from 2006 in there and its running windows 7 with 3 gigs of ram, and a nvidia gt220 card. but last week it started to randomly chrash to where i cant even move the mouse, Completely irrecoverable, and now it wont even turn on. I know it has power because my Wireless adaptors lights Stay on and there green, normally they flash but now there just staying on for however long i wait before turning the psu off. I think its the motherboard :( or cpu
Mother board is ffrom a HP a1610n with the cpu it came with
 
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