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First of all, I am very sorry this has happened to your computer.
This is an indication of a hardware failure. Potentially the motherboard. But more specifically the Video processing components.
I suggest, you run a series of hardware diagnostics, on a very low level. Meaning that you run the tests BEFORE windows boots.
The ULTIMATE BOOT CD, is a free utility that has a myriad of these types of tests, but many others of the freeware kind are available.
This is where you should start, and ultimatley find, and then fix the issue.
Ultimate Boot CD?
find it here:
Precisely, you can download it for FREE, and then burn it to disc yourself. Or you can PURCHASE one, and have it shipped to you. Just follow the link for ALL the details.
If you had a regular desktop, I would say NO, its not too bad. But because you are using an All-in-One, you cant just run down to best buy, for a new motherboard. Because all-in-ones are VERY proprietary. So, an all-in-one is going to be MORE than a normal desktop.
Most likely, you will have to order the part from Gateway.
But hopefully, and you should check, it is still under extended warranty??? If so....repairs are free.