I've seen batteries go bad after 5-10 years. That takes very little to fix. Hard drives might fail after a few years if you buy the common, cheap machines. At work the monitors probably go next as they can fade out. You might then have a power supply problem. The motherboards and cards don't fail all that often.
All of my machines are still working. I have an Apple ][ with floppies and hard drives, a 286 24Mhz PC, 486 DX2-66Mhz PC, and a PIII Xeon 500Mhz PC. The PIII with its non-Windows GUI will outrun my 2Ghz Windows 2000 machine at work. I prefer to move drives to new machines and copy the drives, or just leave them in the new machine. I also leave my machines on, but they have drives that are made for continuous use.
My car mechanic has several Best Buy PCs at his shop and they are fine after several years. He usually runs out of space on his HD first. A UPS is also very helpful in keeping a PC physically healthy.
Buy your new PC. If the new PC can't handle your old drives, just add a card for that. Install the old drive(s) in your new machine and copy the data over. When you're done just put the old PC back together and erase it if you plan to get rid of it.
Another modern solution to the need for a LAN is just a CDR/W and a pack of disks.
David