|If you have NOT been fiddling with anything inside the case before this first happened or since.....|
It probably has a BESTEC power supply and that power supply is probably failing.
If you replace the power supply before the BESTEC power supply fails completely, you have the best chance of the computer working fine again.
If you have another working desktop computer you can borrow the power supply from, or if you can borrow one from a friend's computer, try that before buying a new power supply.
BESTEC power supplies malfunctioning or failing completely are probably the number one reason desktop emachines computers fail to boot normally. They have a reputation of being a lot more likely than average to damage other things when they do that, especially when they fail completely - they often fry the motherboard, or worse.
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:
If you have a video card in a mboard slot.....
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.