If that's a PCI-E card it shouldn't need a power connector. If it's an AGP card, then yes it does need an external power connector. If it has a 4 pin molex connector on the back of the card then you need to connect it. Your power supply should have some 4-pin molex connectors. If none are free, then you need to get a splitter to share one with a CD-Rom drive or something. If it's a 6-pin PCI-E connector then you need to get a 6-pin to double Molex adapter. Of course, that's not really ideal and it may be better to get a new PSU, especially if the one that came with your Dell is weak. You can get adapters and splitters at your local CompUSA or online from Newegg.
If it has an auxiliary power connector on it you need it. Without any investigation (I'm lazy), I am going to assume that this is an AGP card. The AGP bus can only supply 6A (if I remember correctly going off the top of my head) on the 3.3V line. This isn't enough to supply the card power, thus the external power supply connector. If this is your card:
The beeping is normal. If the card doesn't detect power at the auxiliary power connector it tells the motherboard that the video card has failed. Once you plug that connector in, it should boot up just fine.