Welcome Rusty K,
I had the same machine a while back when I was starting on computer recording, except it was a 400MHz celeron. I put in an extra 32MB for a total of 64MBSDRAM. That card in it now gives lots of hiss, so I tried a darla 24 by echo, and with ntracks software couldn't even get through recording one stereo track over 1 minute. Keep in mind that I was just starting to learn this stuff and am still not real learned on computers, so I sent the card back to echo and got a different computer. I do know that I was able to take out the old soundcard and put in the new one though, and I have heard of ways to increase performances of celerons (not sure if thats what you have though). You may even try to look into upgrading the drive and or processor and RAM. With that crystal soundcard though, I was able to get about 13 tracks playing back with ntracks software at 22.1 bits in mono, but again the hissing was pretty bad, and sampling rate low and in mono. I did measure the room inside it the emachine I had, and had to rule out a card at Gadgetlabs I was looking at.
I hope you will have some luck with your needs and the emachine. By the way, are you wanting to record with the digital 4 track and then send it to the computer for editting etc, or are you wanting to record with the computer? There is some really good help here at these forums, so just keep asking questions, and tell people what you want to do with your setup, how you will be recording, how many tracks you would like to hear playing back, maximum number of tracks you might be recording at once, equipment you have, how much you are willing to spend, etc. and they will lead you in the right direction.
bobbo