Did it work until you installed that memory module, or was it misbehaving before that time?
First, you want to dissipate all residual power and influences. Press the power button and hold it down a long time... up to two minutes. That will discharge all power that might contribute to the issues. Then attempt a restart. Do you get a flash of light on the screen or the power on button, that quickly (three seconds) goes out?
Some problems that may or may not be relevant here. That model has a screen inverter that goes out after a couple of years... and makes the system dead. How old is the computer? Did you have any issues with the screen changing colors or having an uneven appearance.
Second, the board may have a power jack that has come loose from the system board. Do you detect any "looseness" when you plug the power adapter into the computer.
Sometimes a failing battery will cause problems. Try removing the battery and note whether there are any differences.
Power adapters in Compaqs go bad way too often. You can buy one on eBay for $12 but that doesn't help you today. See if you can find someone with a similar power adapter for a quick test.
Common causes are bad hard drives... but you need another hard drive to test... They cost about $55 at directron.com, zipzoomfly.com, frys.com, pcmall.com, newegg.com, tigerdirect.com and others or about $70 in town at your computer store.
One bad memory module can be the cause, and some memory modules are hidden under the keyboard. Try moving the memory modules to different slots.
The point is that it can be a number of possible causes, and it takes some time to figger out which is the one. Usually it is simple, but the screen inverter is difficult to replace, though cheap to buy. The common causes for that machine are failed hard drive, failed memory module, defective battery, defective power socket, and failed LCD inverter which is behind the screen at the bottom of the screen when open. You cannot get at it unless you remove a lot of screws and screw covers. Do that when all else fails.
Keep good notes about what you try. And get back to us for more wild and crazy ideas.
Your Compaq is no worse or better a laptop than a Sony, HP, Toshiba, Gateway, Asus, Acer, or Dell. All laptops fail now and then. Figgering it out is the time-consuming part.
Just keep good notes so you can recall what you have tried. A lot of the work in Laptop repair is in ruling out possibilities.
Eventually, you can fix it, unless you have spilt liquid into the keyboard that has shorted out the board.
