I wrote a large article with images and explanations of each piece of hardware and connection. I dont feel like going over the same thing again so here is a brief overview of my advise.
First of all, chances are you have an IDE hard drive. I doubt that its old enough to be DB25. The likely connections that I could see are:
IDE
Serial ATA
However the following may confuse you:
SCSI
Raid Array (Whether its IDE, ATA, SCSI)
Some people have built machines using adapters to use Laptop Hard Drives, this may also be an issue.
Furthermore I've seen some people even use SD cards, Express Bus,PCMCIA (Rare) with adapters when on a budhet and using spare parts,
My advice.
1. Find the type of Hard drive and buy an enclosure for it. They are $15-25 dollars and can be connected via USB, Firewire, ISCSI etc.
2. If the old machine is operable you can either shhare the drive on the nework or use a crossover to connect both machines. Set PC1 to static IP 192.168.1.1 and PC2 to 192.168.1.2 and then eplore your network or use: net use z: \\ 192.168.1.x
Further more you could click start, run, type the IP or DNS name and add the hard-drive by mapping it and doing a transfer over night.
The easiest of all is simply buying an enclosure. For future reference I highly suggest purchasing either a 1TB external for backups or a file server like a Terrastation.
Cheers