That sounds an awful lot like a stick of bad memory (RAM). Check this link out, it has a guide as to how to use that software.
How to Use Memtest86 to Check for Bad Memory (RAM) in a PC
If its not ram, try the following
Try opening msconfig (Start>Run/open>msconfig), click the startup tab and disable everything. Restart your computer, and see if this resolves the issue.
***********************************************************
Another thing to check out is power saving settings in the bios, be careful in here if you do not your way around. You hit either the F1 or F2 key for gateways I believe to enter the bios. Check the power saving settings and make sure it doesn't have sleep mode settings. If you change something on accident and don't know what the setting was, simply "exit without saving changes." If you make a change that you want to stick, "Save and Exit."
The problems you are having is why I do not buy Dell, Gateway, etc... you are always money ahead to buy a case, non-proprietary motherboard, and whatever components you may need and put it together yourself. If you are not comfortable with that, chances are there is someone who lives near you who enjoys doing this sort of thing for a modest price.
Read reviews about the build quality of every component, choose wisely, and you will end up with something that will last you a lot longer than anything you can buy from a big-volume computer mfg. There isn't a lot of money in designing something to last a long time. They often fail just outside of warranty because that is a lot better for their bottom line than selling something that lasts a great deal longer.
I hope some of this is helpful to you. No more buying mass produced computers.