Just out of curiousity, how much of the specs can you remember? Right down to the modem brand and model, or just the major specs (processor, videocard, RAM, hard drive)?
Off the top of my head, the first PC I owned all to myself (not a family PC) was:
AMD K6-2 300 Mhz processor with 3DNow!
ATI All-In-Wonder videocard (with ATI's Rage chipset)
128MB RAM
WD 8gb hard drive
Soundblaster audiocard (obviously)
SCSI Pioneer 1x-2x CD-R (not RW) was connected to some generic SCSI CD-ROM drive (remember when you used to copy CD-to-CD? lolz)
3com 10/100 Mbps network card
Modem -- don't remember the brand, but I know it was an ISA-slot card, and ISA was dying at the time as a standard
For 1998, I guess it wasn't a bad machine. I remember I really wanted an ATI TNT, but the dudes at the shop said it wasn't working with the other stuff in there.