Very first thought I had was there is a CD in your CD drive and the bios is somehow set up to check the CD rom first when booting.
I know it sounds stupid but you would be surprised how many people have just left a CD in the CD rom and had problems with the computer loading up or going slow lol.
But it sounds like you checked all of that.
E-Machines were set up to be very cheap computers and in many ways you are lucky it has lasted.
We got some for our workplace about 4-5 years ago and it was a pain in the butt to find drivers that were never included with the PC....they did not even include all the drivers for the motherboards video and audio. The video was easy to find...the audio was not...and it was found later but not on the e-machine website.
You may get lucky and just have to get a new Hard Drive...of the 5 we got we have had to change the hard drive on 3 of them already...they just went dead.
But if you got the money just get you a new computer...you will be better off in the long run. But if money is tight get a new hard drive even if someone can fix your computer a new hard drive will be better.