> some unnamed AGP video card
Do you mean VGA rather than AGP? AGP came much later than the 386 and wouldn’t have been supported by its motherboard chipsets.
Probably correct, though I think I had a 486 board with an AGP slot? I didn’t have anything newer than that until the Core 2 Duo came out.
Same size as a normal ISA connector but "deeper" (2 rows of contact if you could inspect them)? EISA
Full ISA connector (potentially missing the bit in the middle) and then a further piece? VLB
Shorter than ISA but higher density? AGP (it's even a bit shorter than PCI)
Was it at least a Pentium? Can't be AGP otherwise.
Going to ignore PCI-X, PCIE and obscure AGP variants