This could be any number of things, including your motherboard, your graphics card (if you have one), or your RAM. The first step, I think, would be to try using memtest, if you can.
This is going to be written assuming you have access to a Windows computer to use. If not, let me know what you're using to post here and I'll see if I can help you out.
Step 1: Go
here. This is the download for the memtest ISO file.
Step 2: Go
here. This is the download for ImgBurn, which you'll use to burn memtest to a CD or DVD.
IMPORTANT: CAREFULLY read each screen on the installer here. ImgBurn unfortunately includes OpenCandy, which might try to sneak some other software into this install.
MAKE SURE YOU ARE ONLY INSTALLING IMGBURN. You may also want to scan with Malwarebytes when you're done to make sure you didn't miss anything.
Step 3: Install ImgBurn.
Step 4: Go to your Downloads folder. The path should be C:\Users\[Your user name]\Downloads. Right click on the memtest86+-5.01.iso zip file. Choose "Extract All". Extract to wherever you want, although I suggest the Desktop for easy deletion when you're done.
Step 5: Put a blank CD or DVD into your computer's CD or DVD drive. Your local office supply store should have blank DVDs if you don't.
Step 6: Open ImgBurn. Choose "Write image file to disc". Under Source, click the Browse for a File icon, then navigate to your extracted memtest folder. Choose the ISO that's in it. Make sure the destination matches your CD or DVD drive. Click the Write button.
Step 7: As soon as it's done, take your memtest CD or DVD and put it in your laptop's drive. Turn your laptop on and mash the Boot Menu key. On Gateways, I think it's F10; if not, try the escape key or F12. When the boot menu comes up, choose your DVD drive. If you're having trouble figuring out which option is your DVD drive, let me know what the options are and I'll tell you.
Step 8: When memtest comes up, let it run overnight. It's best to let it do a few passes so that we can get a better idea of whether or not your RAM is okay. Post back here with memtest results. If you can't get to memtest, I'll want to know if your machine is POSTing or not.
If you have any questions, let me know.