Hey Bob! I have a gateway MT-6821 with the EXACT same problem you described. I took your advice specifically as stated, and it worked. For those of you are still having trouble, with tictactoe's advice, here is what I did after multiple failed attempts until I found Bob's advice.
1. Remove power supply and battery.
2. Hold power button down for 30 seconds.
3. WHILE STILL HOLDING DOWN POWER BUTTON, INSERT POWER SUPPLY (that's what she said), THEN INSERT BATTERY. *THE POWER BUTTON SHOULD BE HELD, THROUGHOUT THIS ENTIRE STEP.
4. At this point, the blue light and the charging light both came on, and the computer started properly.
Everything Ran normally after that!
Thank you to everyone who posted on this blog. It seems that Gateways have trouble following tictactoes's original advice but this, slightly modified technique, worked perfectly for me!