|Please tell us which Gateway model you have.|
The specific model of a brand name system is often shown on a label on the outside of the case somewhere.
I'm assuming you have NOT touched anything inside the computer case since the computer last worked properly.
If you HAVE, tell us what you did.
A common thing that can happen with ram, even ram that worked fine previously, is the ram has, or has developed, a poor connection in it's slot(s).
See response 2 in this - try cleaning the contacts on the ram modules, and making sure the modules are properly seated:
If that doesn't help
Unplug the case/power supply, or switch off the AC power to it otherwise.
Power off your monitor.
Open up the case by removing the left side panel as seen when you're looking at the front of the case.
Check all the connections of the wiring to make sure they are all the way onto their pins and into their sockets, especially the main connector from the power supply. The wires close to the mboard going into the main power connector/socket should be more or less perpendicular to the mboard surface rather than at an angle. Make sure all cards in slots are all the way down in their slots.
Some cases have a latch you must push one way rather than screws you must remove at the back of the case.
While you're in there, if the cpu fan/heatsink has mung (dust, lint, etc.) on it, clean it off, but DO NOT use a vacuum cleaner to do that (they produce a tremendous amount of static electricity when running, and anything connected to them can discharge that to your components) - use canned air, or an air nozzle if you have access to an air compressor, or an artist's brush that can be used in small spaces, etc. It may be difficult to clean the top of the heatsink under the cpu fan - the most likely place to have mung on it - and the bottom side of the cpu fan blades unless you remove the fan. If you have a case fan, clean that too if it needs it.
Also check for mung on the video card fan and heatsink if it has that, and the power supply's openings / fan.
With the cover still off, restore the AC power, start the computer and make sure the cpu fan spins - if it doesn't spin, if you're sure the power supply is working okay, don't use the computer until you have replaced it.
If it spins too slowly, and/or if it makes rattling or screeching noises, most likely to be noticed when the computer has cooled to room temp, has not been used for a while, and then is started up, the cpu fan's bearings are failing - the cpu is likely to overheat as a result of that if it can no longer spin it's full speed - replace it as soon as you can.
If that doesn't help....
Failing power supplies are common and can cause your symptoms.
Check your PS.
They often partially work, fans and hard drives may spin, leds may come on, yet you may get no video and the mboard will not boot all the way.
See response 4 in this:
If you can borrow a power supply from another working computer, try connecting that.
If it is failing, you can usually replace it with any decent quality standard sized standard ATX PS with the same capacity or greater.
Standard (PS/2) power supply size - 86mm high, 150mm wide, 140mm deep, or 3 3/8" h x 5 7/8" w x 5 1/2" d , or very close to that, though the depth can be more or less for some PSs.
Don't buy an el-cheapo (in quality) PS.
See response 3 in this:
Your power supply must have at least the minimum capacity required to support a system with the graphics card you are using installed, or the max graphics card you might install in the future.
(Onboard video - video built into the mboard - IS NOT A CARD ! )
If that info is not in the ad for the video card, you can go to the video card maker's web site and look up the specs for the model - often under system requirements - the minimum PS wattage, and, more important, the minimum amperage the PS must supply at 12v is stated. If you don't find that, any card with the same video chipset including any letters after the model number has very similar minimum PS requirements. Some power supplies have two or more +12v ratings - in that case, add those ratings to determine the total +12v current capacity.
If you're a gamer...
In most if not all cases, the max capacity rating of the PS is an intermittent rating. It's recommended that you do not load your PS to any more that 80% of that rating if you are going to be using something that puts a constant load on it, such as playing a recent game for hours on end. In that case, you multiply the min capacity stated for the system with the particular video chipset on the card by 1.25 to find the min. capacity of the PS you should get.