Recent years computer all comes with PCIE so chances are, its the casing
I know cause I have a god damn small casing. Mind you these days, casing are so short, even though it meets the medium size ATX spec, that's just the height. 4 CD bay, 2 floppy, 5 hard disk, yeah.. but the length of the case is pathetic.
Unfortunately, no, you cannot fit the card in without changing the casing. 4650 is indeed a long card. You can't cut the card or so. I wouldn't say cutting out the hard disk bay to be a good idea too, lol.
I changed my casing to ensure it can fit a 9800GTX+. Its the best option.