|Has this laptop been dropped, or otherwise subjected to a physical jolt ?|
Has it had liquid spilled on it, or has it been exposed to liquid such as rain, or has it been sprayed with liquid ?
(It doesn't matter whether it was running at the time. If as little as just the battery was installed, it could still have been damaged because of the liquid. ATX mboards are always powered in some places, even when the computer is not running, when the power supply has power to it.)
If anyone else has had access to this laptop since it last worked properly, if you didn't do those things, it's possible they did, and haven't told you they did that.
According to a tech who posted on this site, those are the most common reasons a laptop is damaged such that the mboard or other components inside the case need to be replaced.
An internally shorted (main) battery can cause all sorts of problems, but removing it and connecting only the AC adapter should eliminate that as being a possible cause.
"connected a monitor and Fn lcd/crt switch"
Problems with the built in display are common after the laptop has been used a lot, but if nothing else is wrong, connecting an external monitor should produce a display on that, assuming you pressed the right key combo.
Incompatible ram or improperly seated ram can cause no video and no mboard beeps.
You could try removing the (main) battery and the AC adapter and re-seating the ram,
or removing all the ram then attempting to boot the computer - you will get no video but if nothing else is wrong you should hear a dfferent beep than you normally would hear, or a beep pattern that indicates a ram problem or no ram is installed.
Note that some recent or fairly recent laptop mboards produce no mboard beeps in any case - they blink leds to indicate what the problem is.
You can often buy a used mboard for your model from the web for a reasonable price, but you need to determine the proper part number for it - that's usually on a stuck on label on the surface of the mboard somewhere.
If Gateway has no service manual on their site for the laptop series, you can usually find one on the web for free or for a small fee.