Remove the hard drive from the old dell, and it may, cross your fingers be able to be placed into your new e machine or beside it. Power supply will be the same, only cable that may be different is the data supply. I have seen on the internet a cable that takes an old hard drive and hooks it to a usb port. Your new computer then will recognize it as a new drive automatically at start up with just raw data.
As long as you were not running Linux, Sun Microsystems, Unix, or any other non microsoft windows operating systems on that disk, you will be fine. Whatever you do, do not reformat the disk or place anything magnetic around it, bounce it, get it wet. I had a windows 98 machine, and took the hard drive out of a compaq presario and hooked it directly to my Microsoft professional 64 bit machine I built from scratch and I was able to pull all of my files I wanted off. By hooking it direct, the computer saw it as a source of files only and the file transfer was very simple. You may also have to have the same or similar computer programs to recognize files that you have on your new machine.
For instance, open office, which is downloaded for free at www.openoffice.org
does not always allow all microsoft office suite files to upload fully with all of the bells and whistles of word, excel, powerpoint. But also there is no way in this green earth that I am paying 300 bucks for something that I use once a year when I can get a basic free version. On Word, when searching for older office files, you also have to change the search functions to look for the older file formats if you are looking for word files, and the same is for powerpoint, excel and other microsoft programs. If you want to save yourself some money, use the openoffice instead of buying it if you have to.
I have a co worker who bought an e machines from wal mart. He is already having trouble with the dvd burner. Make sure everything works, or else you wont be having much fun. Computers can be really frustrating. BTW, are you running on the amd athlon, sempron chipset. You may want to check out www.amd.com
if you are not running on the 64 bit microsoft xp operating system which has been out since, July. Programs, and especially large files run really well with the 64 bit operating system, much faster. I ran the xp, until I was able to upgrade and it is noticeable. Virus protection is a little slow right now, with mostly www.avast.com
offering a free virus protection for 64 bit xp machines. The good news is, its kind of like the macs, there are not a lot of 64 bit machines out there.
As far as networking, you may need to configure your new computer to register as being on a network through your control panel. Hope any of this makes sense, but a few things to look at.