Hi rescun3351
It's likely a hardware failure, as most of the hardware is likely from the 1998-2000 timeframe, and is now eight years or so old.
If you aren't hearing a single "beep" during the first few seconds upon starting the computer, and the PC never proceeds past that initial Bios banner, then it's not able to pass the Power-On Self Test (the "POST") that standard PCs run every time you start them.
Try unplugging any extraneous peripherals (printers, cameras, scanners, multifunctions, PDAs, USB flash memory drives, external hard drives, etc.) and see if the PC can progress any further in the boot process.
If not, the Dimension 4100 has some diagnostic lights that might help. These are located on the back of the computer - very close to where you plug your speakers in. There are four little LED lights in a little rectangle --- depending on which lights are certain colors, they might be able to tell you what part is having trouble. Here's Dell's guide to reading those diagnostic lights ---
http://support.dell.com/support/edoc...agnostic_codes
It's not likely to be financially effective to replace failed parts, as such old parts are now rare, and can be expensive. Should you be able to find some old spare parts for free, then repairing your classic might make sense -- but you'd have to be prepared for other parts in the system to fail eventually as well. This sort of thing is fun for PC enthusiasts (I keep various old relics running just for the fun of it) -- but the need for lots of maintenance is a real drag for anyone who'd have to rely on such an older machine for important work.
If it turns out that the PC isn't salvageable, try to get it to a recycler, or to hazardous waste (PCs contain dangerous substances & can't be thrown away in regular trash).
Best of luck!
. . . Gary