As previously noted, you are likely to be best served by purchasing a new computer.
If you have any licensed software on your old computer, I would suggest recording the serial numbers (a text file work great) and download the latest versions that work with those serial numbers to a USB flash drive, external hard disk drive, etc., they will be ready to install when you receive your new computer. Don't forget the anti-malware software as well, just in case your new computer doesn't come with any (or if you want to replace what comes with it with your preferred software).
Before you use the new computer on the Internet, be sure to run Microsoft Update to install whatever updates, patches, hotfixes, etc., are available for it, as chances are it is going to be missing a few of the newer ones. If you buy a brand name computer (Dell, HP, Lenovo, etc.) it may come with an additional manufacturer-specific utility to update its drivers and model-specific software. Be sure to run that as well.
From looking at the specs, I believe the Dell Dimension 4600 shipped with a PATA hard disk drive, which means you'll need an adapter of some sort to plug it into your computer to copy your data files off of it. Of course, it might be a different type of drive if that's been replaced over the past ten years. In any case, there are USB to PATA/SATA adapter cables which can be purchased for around $10-20 that you can use to transfer the data.
Another option would be to connect both computers to a router, switch or hub and copy files across the local network from the old computer to the new, but this implies that you have a keyboard, mouse and monitor set up on both computers (or can easily move them between the two computers) and the space to do so. If you don't, pulling the drive as mentioned above might be a better route for you.