Whip out the hard drive from the Windows 98 based computer, and stick it into an external USB caddy that'll plug into a port on the Windows7 PC. Not that difficult, just a couple of screws on the inside of the case (unless it's a laptop), and pull the cables on the back.
Not sure if you'd be able to connect the Win98 Hard drive directly into the motherboard of the Windows7 PC, as back then they used "Ultra ATA IDE" cables, while Windows7 machines had generally switched over to using "SATA" cables, and no guarantee there's any legacy support on the motherboard to plug in an old style cable if you need to.
But you can get external hard drive caddies you can insert a hard drive into, and they're available in "Ultra ATA IDE" connector versions or "SATA" versions, depending on the connector on the hard drive.
That's how I've transferred stuff from the hard drives on my last few PC's... stick it in a caddy, and connect it as an external hard drive.