Problem with Computer, possibly MoBo

Hi, I've been having some problems with my Family's PC, it's steadily grown worse over the past month, First it started as the computer just randomly turning itself off, sort of... power was still going through it as the power ligths were still on fan going etc etc but nothing, not just the screen going it was as if it'd been reset but not posting. now it's got to the point where after 2 minutes of being on, it turns itself off, won't and won't post, I tried hooking an external HDD in the hopes I could back eveything up before it died (Irony) and it's still on despite being turned off. I can hear the spindle in the HDD turning when it's plugged into the USB.

Unfortunately I can't tell you anything else about it other than it being an AMD spemron CPU and a Packard bell machine, I've got my own PC and laptop so I don't bother with the family one. I'll know some more when I open it up tonight to have a look inside. My parents have suggested the power but I don't think it's the PSU, if it was it wouldn't even start right? I'll test it with a spare one tonight when I open it up.

Yesterday when my dad started it up it got to the splash screen however it had lines going down the screen. not sure what else I can say about it really.

Personally I think it's the MoBo but I don't know any ways of testing it.

Any suggestions would be very helpful

I've fixed it now, swapped it over for a spare PSU I had and so far so good. however thanks for the suggestion anyway.

Now my parents owe me a new PSU... looks like they're gonna have to pay £150 for a new one

(they don't know anything about computers)