PCI-E and PCI are completely different. so is AGP.
you won't be able to use a 7800 GT unless they make an AGP version of it.
PCI is an older slot, still widely used but not by graphics cards. that's because it is just too slow for them. but it's fine for things like network cards, modems and such.
AGP was made because PCI was too slow for graphics cards. it is made for graphics cards only and is a lot faster than PCI. AGP comes in 1X, 2X, 4X and 8X. you can use 8X and 4X cards in 8X and 4X slots, you can use 2X cards in 2X slots, and 1X cards in 1X slots.
PCI-E is the next slot designed to replace both PCI and AGP.
currently, there are 1X, 4X and 16X slots. these speeds are not the same as AGP speeds. PCI-E is one or more serial connections to the card. with one lane going each way on a 1X slot, 4 lanes going each way on a 4X slot, and 16 lanes going each way on a 16X slot.
each lane gets 2.5GB/S each way (5GB/S both ways), a 16X lane getting 40GB/S wach way (80GB/S both ways) compared to AGP speeds which are as follows:
AGP 1X = 266MB/S
AGP 2X = 533MB/S
AGP 4X = 1066MB/S (1.1GB/S)
AGP 8X = 2133MB/S (2.1GB/S)
__________________  1 + 1 = 3 if you define 3 as a result of 1 + 1
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