Gateway laptop Model MT6705

Hello,
My Gateway laptop wont turn on today. Its been plugged into the wall almost consistently just because my battery life depleted some time ago, so I always keep it plugged in. Yesterday I did notice that the power chord /the square block/brick portion did seem a little warm.
Today when I hit the power button , the battery sensor light at the front flashed red 3 or 4 times & does nothing else. The computer feels completely cool to the touch today.
Things I've tried:
Leaving it charge for a half hour or so to see if it would take enough charge to turn on= no repsonse

Removed the battery for about 10 minutes & unplugged the laptop. When I reconnected the power chord ( battery still not installed back in) the blue light around power button came on. So I went with it & hit power button and it seemed to be turning on , went through to the gateway welcome screen which comes on right before your desktop loads, then suddenly it just shut down. Then I tried re-inserting battery to see if that would help, still no response.

Next unplugged laptop & unplugged power chord from outlet, removed battery & let it sit for about 10 minutes . Then I tried the method of holding the power button for 30 seconds & rebooting. (did this twice because Ive seen 2 different tips on how to do this. One with putting battery & plug in before attempting a reboot 2) Just plugging it in, turning on , then inserting battery. Either way, I had absolutely no signs of life after trying this.

The only response I get is that red flashing light when I hit the power button. Do you believe this is a power chord issue and/or battery or is this something more. The computer is no spring chicken, although Ive never had any problems with it & a new laptop isnt in the cards right now.

Any help would be appreciated!