How are you going to put the card in if you don't open it up? Perhaps whoever is going to do that should have a look inside before you buy the card
(but no, you don't have to open it up at this stage, as you should be able to get the specs if you know the exact model number of your computer, and then have a look on Dell's site. The other thing to be wary about is whether your computer only supports 'low profile' cards - is it comparatively thin, or is it as wide as they get?)
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By the way, it's not 'AGP or PCI' - it's either only PCI, or AGP and PCI. However, since AGP is a much better way to connect a graphics card, you don't want to get a PCI card unless you have to.