If the fault is persistent, then there is a serious startup condition to be resolved. The suspects I'd suggest in no order of likelihood are:
1/
Your graphics card which presumably has its own BIOS and does a lot reaching into main RAM

2/
Your motherboard RAM esp. if it's Value RAM which is of unguaranteed quality IMO.

So a bit of device swapping might be your best first step. Might not be cost free if it's the graphics card.

Try removing each RAM stick one by one then put them in one by one in each slot to see if it is the RAM or the RAM slot at fault.

... and I'd put a fiver on the graphics card!

How much RAM do you have, and what is you Graphics Card?
This could possibly be an overheating issue, how many fans are inside your computer and what size is your CPU and your PSU?

its a 15 inch gateway laptop with an integrated intel graphics processor (intel gma 950), 1gb ram dual channel, and a 1.6 GHz intel centrino duo.

Hardly likely as this happens when he starts up.

It's likely to be a bad component that addresses or is memory. Dosen't matter what CPU or RAM size he has because this is happening at boot up.

The fact that it's a laptop and integrated graphics processor narrows your simple fix hopes to the RAM.

Then I'll try swapping the RAM modules...But if that doesn't work, any other ideas?

It'll either have to be repaired by Gateway or replaced IMO. I just can't see how this fault can be anything but hardware.