Dell laptop inspiron 1545. black screen and booms out 2 SHORT beeps.

0786030,
The 2 beep code error represents a memory error. Try reseatting the memory in the computer. If that fails, then you may need to replace the memory.
Thank You,
Dell-Jesse L
Dell Social Media and Community

1) your power supply is shot if the new GPU required more power than your old one could deliver
2) you may have statically shocked a component or four
3) a simple loose cord either for GPU/CPU/ETC so you may have bumped something

Try to find either the user manual, or at least the full specifications of that machine. The user manual may list what are known as POST codes. If not, the specifications should list the BIOS maker (PHONEX, AMI, ETC), for which you would look up their POST codes (i.e.: google "ami bios" POST codes).

FYI: POST codes are built into the computer's BIOS, and are used to send out Morris code like beeping sounds through a small speaker on the MB, to indicate a hardware problem that he BIOS has detected.

If the POST code turns out to be a video hardware problem, your probably SOL, unless you happen to have a high end laptop with a removable video card. Otherwise I would guess it is a memory problem, and you should try to remove and then re-seat the memory module, or replace it/them.