You may need a sata pci card to enable the sata hdd.
Why not install Windows on the 80gb drive.
I have no experience with these adaptors to know if they are detected as sata or ide. Can you return the the drive and exchange for an ide one?
If not you can still use the old 80gb to install, get a sata usb powered case for the new drive and use it for backup, video, photos and audio files.
Installing XP on a sata drive requires a sata driver to be installed when prompted during instalation.
Some of these converters come with a jumper to select IDE Master/Slave/Cable Select, it's worth checking the manual (if you have one) or doing a Google; also check the SATA interface speed (on the converter), some only work with SATA 150 drives (SATA 1) and the drive may have to be jumpered to reduce the interface speed.
Check the jumpers on the drive, it may need to be set to SATA 150 as someone suggested, and check the jumpers on the converter. I don't have much experience with drive converters, so I really don't know what to tell you otherwise.