Sure thing

If it came down to it, we could try to determine if your existing power supply uses a standard ATX plug. They have 20 pins (two rows of ten pins) to deliver the power to the board. If the arrangement of the wires matches that of a standard full-sized ATX power supply, then you could conceivably transplant your VIAO's insides to a new standard-ATX case with a new power supply.
Of course hmm, the CD and DVD drives look to be somewhat proprietary, ditto for the floppy...

and down the slippery slope we go. Suddenly the mobo, CPU and existing memory become the
only parts being retained and heck, at that rate, why not replace them too... so it becomes a can of worms fast. You're left with a butchered Sony, whereas you could restore it from its Restore CD's and sell it in one piece to get some money out of it.
Just off the top of my head, some stuff that could fit your needs if you cave in and decide to go for the full bang-for-buck upgrade:
Antec SLK3700AMB case with SL350 power supply $85 (shipped)
Shuttle AN35N Ultra motherboard $55
AthlonXP 2500+, retail $80
512MB Crucial PC3200 memory, one module $105
Radeon 9800 Pro $210
Hitachi 120GB 7200rpm hard drive with 8MB cache $85
Lite-On SOHW-812S 8X DVD burner (black), retail-boxed with software $90
Sony floppy drive (black) $12
Windows XP Professional $135
Ouch, about $860US!

But it would be an upgrade in more ways than just its gaming capabilities (you get a DVD burner and a big, faster hard drive). You would lose Firewire (substitute an Abit NF7-S motherboard for Firewire and the SoundStorm hardware-accelerated audio if desired, add about $45).
Another option would be the Shuttle MN31N motherboard, which has onboard GeForce4MX-level video (two monitor ports, even) plus an AGP 8X slot. The beauty of this one is that 1) it comes with Firewire and the hardware audio processing, and 2) since it has onboard video that will eat your TNT2 M64 alive, you could pick up the Radeon 9800 Pro a little later when its price has dropped, thus easing the all-at-once cost by $210. The drawback to the MN31N is that it doesn't have support for the two AthlonXP's that use a 400MHz bus (the 3200+ and one of the 3000+'s), and is not as much of an overclocker.
I had better stop before I drown you in Too Much Information

but I hope that was some help.
EDIT: one other remark... if you do pick the MN31N with the intention of using its onboard video for a while, then getting two 256MB memory modules will increase the onboard video's 3D capabilities by about 50% because the motherboard can run both of its memory controllers when it has two (or three) modules, and that lets the onboard video hit its stride better. You could later add a third module, probably a 512MB one, to fill 'er up to 1024MB total when the need arises. Some current games and certainly some future games will take advantage of 1GB of memory, so it's nice to have an upgrade path available.