That's BIOS trying to tell you there's something wrong before it can print anything on the screen.

That's why it's using beeps.

Look in your documentation for the meaning of 4 beeps.

At least it came through POST, else it would present a flash code at the keyboard lights.

Did you upgrade your BIOS also?

I don't know where the documentation is for this laptop and I tried searching online for the meaning of 4 beeps but couldn't find it.  I did upgrade the BIOS.  

See the support section of the DELL site for manuals.

Case the laptop plays dead after BIOS upgrade, seems to me the upgrade went sour.

Recovery from dead bios is a lot of reading and trying.

Good starting point is here http://www.wimsbios.com - go to the forum

I ended up running the Dell Diagnostics utility, not really expecting a result from it, but worth a try since I didn't have time to do much else to it yesterday.  It ended up coming back with a keyboard error, one of the keys was stuck.  And that was the problem.   :P

If the BIOS update did complete (i.e., you CAN boot the system):

Remove the battery and power.  Hold the power button for 30 seconds and restart.  If the beep continues, reseat the memory modules and video card -- if it continues thereafter, you have either bad memory or a bad video card.

If the system DOES NOT POST to a boot screen and the BIOS update did not complete, replace the system board.