Lapdesk11, please refrain from making 3 forum topics trying to address the same question.
Face2Face has the correct answer and solution:
your dell has a ExpressCard 54 plug in solution that will work with
http://www.gearbest.com/laptop-accessories/pp_229102.html . The problem lies in the fact that at best the ExpressCard slot is PCI-e 2.0, effectively giving you at most 500MB/s of bandwidth, but I assume the ExpressCard slot is PCI-e 1.0, effectively giving you a maximum of 250MB/s of bandwidth. The reason we're talking about the Dell is because the HP model you mentioned only has a PCI-e MiniCard solution; any external graphics solution would be limited to PCI-e 1.0 and would require an external wire plugged into the internal components of your laptop (meaning you'd have to screw a panel off and on everytime you would move the laptop from its station, not to mention the ergonomics of plugging in a cable into the internal board through a small panel).
You would need a graphics card, and a power supply. The major issue is not connecting everything, but that the interface you're limited to is not a viable solution, as those interfaces would severely gimp whatever GPU you would plug in. Modern graphic cards are gimped even at PCI-e 3.0 x4 (4 lanes, giving a total of 4GB/s of bandwidth). The interfaces you're stuck with are at best 1/8 of that, but more likely 1/16 of that interface.
Bandwidth estimates on napkin math would be 2560*1440 (resolution) * 16 (bit color) * 60Hz (refresh rate) / 1000 (bits to Kb) / 1000 (Kb to Mb) = ~3500 / 8 = ~440MB/s, and that's just driving the display, not even utilizing GPU functions. The HP laptop @ PCI-e MiniCard only has 250MB/s bandwidth, so that wouldn't work. You could reduce the color's displayed on the display to 8-bit, but for your use cases (on the other posts) that would be self defeating, or force a lower refresh rate
Note: I could use someone to double check my bandwidth #'s, but that's just my rough estimate @ 2AM.