AGP ports rarely die... Computer is most likely dead, its quite a bit on the age.
Try to reset the board by locating the BIOS jumper (Clear/reset CMOS) - Its a 3-pin jumper near the battery with 2 pins jumped. It should say CMOS or something simular. Switch the position for 5 seconds, then switched it back (The computer is off, but has AC plugged in) Then see if it'll power up. PS: If you cannot locate the jumper - then pop out the battery(looks like a large watch battery).
2) If above doesn't work.try another Power Supply (borrow one) - It doesn't need to fit the case, but you need to power up the board.
3) If that doesn't work, borrow a PCI video card.
If all 3 things don't work, its most likely dead.
If you build yourself - You can recycle the drives into a modern system for about $150 or so (AMD board = $50, dual core CPU = $50, 1GB RAM = $20, case + PSU since SONY is non-standard and very out of date= $75) = $195