On start up the monitor shows no signal for a few seconds , then goes blank. I have a Gateway GT5228, windows XP

If the monitor is displaying "No signal" it is probably OK, but it can be verified on another computer just to be sure. If monitor is good, the remaining culprits are:
1. Monitor cable.
2. Video card.
3. Motherboard.

The easiest way to test these is by replacing them one at a time with a known good one.

Check the connector, that it's plugged in all the way on both ends.
Then do as scleros said and swap cables/monitors.
Next, if that's not the problem, open up your computer and check that the video card is plugged in(if you have one).

On start up the monitor shows no signal for a few seconds , then goes blank. I have a Gateway GT5228, windows XP
Open the case, if dusty, blow it clean using canned air, such as DUSTOFF. Check the cable connections, blow clean.

If you still get nothing. There are two tests you can do. If you have a laptop handy, or another computer, hook the Monitor to one of them and see if it works. OR, hook up a spare monitor to your system to see what happens. (everyone should always have a spare monitor) If you don't have a spare monitor OR another system to test with, I suggest taking the computer case... the tower, into a shop and have it tested. OR, buy a cheapo video card and use it to test... depending on what the cheapest option is and how tech savvy you are.