My acer 3624 monitor switches off after a few seconds when I switch the computor on .I have tried using an external monitor but the external monitor does not want to work ie it just says no signal please help?

Seems like your laptop's video output may be damaged somehow.

I assume its a laptop? i agree with the last post,if your laptop monitor is not working then you try a external monitor and that also does not work,usually (in most cases) it will be the onboard graphics card these are usually soldered on and exspensive to have repaired unless you are up to doing it yourself.
have it tested buy a pro,if this is the case then you would probably be better off getting rid and replace your machine,sounds harsh i know but when onboard devices go on lap tops they are normally exspensive to repair,unless you can pick up a working mobo replacement. hope this helps...