Here's your users manual:
http://support.gateway.com/s/Mobile/Q106/Blade/8511385.pdf
Start with troubleshooting power issues.
You didn't say how long the computer will run before shutting off. Here's some suggestions for checking for power:
If you can get windows to load, see if the battery charge or status indicator is telling you the battery charge level or if it's charging.
Try removing the battery and run off the power supply alone.
Double check your power supply connection for bent pins, dirt, secure connection etc.
If the power brick has a status light, check to see if it's on.
If you can get into windows, check your power management and hibernate settings.
If you can get it to run for any length of time, try booting into safe mode and check your power management settings and run virus and anti-spyware scans from there.
Just trying some simple things first until we can get a better feel for exactly what going on. Again, you didn't say exactly how long it will stay running. You might also try removing the hard drive and cleaning all the connections to try to eliminate that as a issue.
You can allways Tech support but you must have the computer registered to you.