Once a flash fails, the board is dead - you will need to replace it.  The BIOS chip is soldered to the board and not replaceable.

 Could be to late now but before I tried flashing the Bios I read around in here and found out that I needed the original DELL memory to do so. I had upgraded it to 1GB but after I put the 512 back in it worked like a charm.FYI

Ok i figured it.. Your tip with the Ram Daddy lead me to read some more.. and after googling it found someone else who had the same issue.. Apparently after flashing from a06 to A22 it is nesseasry to fiddle with the ram. i ended up taking both out and using only one stick. after a few times of swapping them it came back to life.  After more than one dell tech told me my board was dead. So maybe this will helpsomeone else who had the same problem

I made the mistake of updating to A22 with my new Dell PC 2700 memory  (2x512mb) installed and had this same problem. Thankfully I saw this post! Reinstalled the old ram (had to try twice with a 246 and 128mb combined) and  normal screen behavior resumed! LOL  I've updated to A32  (fan warning on the initial boot up) but looks like this'll be a successful bios update thanks to a second computer and this community! Thanks!  

In Dell's defense the written instructions included with the official Dell memory sticks recommends the Bios update before installing the sticks. I installed the sticks before updating (without reading the instructs) and they worked fine except for a Windows XP "the system has recovered from a serious error" message occasionally. Then when I updated to A22 the new sticks caused the black screen prob. It wouldn't hurt for Dell to include more specific web site alerts to those actually purchasing the Dell recommended memory upgrades. I understand that's asking a lot with the glut of different probs out there.

WOW!!! This thread just saved my Inspiron 5100!  Got it second hand with a bad hardrive.  Replaced the drive, installed XP Pro.  Noticed it had two 512MB chips (original Kingston chip and an Ultra brand add-on), but was only using one.  Tried switching them around, no help.  Ended up running with only one chip in the SODIMM B slot, the Ultra brand chip NOT the original factory chip.  Tried to upgrade Phoenix BIOS v.2 with Dell BIOS A32, error.  Took almost a year to find the info that I had to boot w/floppy and install A22.  Did that 12/15/09, rebooted, dead.  No video, no beep, wouldn't boot from floppy, CD, nothing.

Tonight, found this thread and I still had the original 512 MB Kingston memory.  Installed the original chip in Sodimm slot A, no boot.  Moved it to slot B, and it booted!  Got the funny heat/fan warning on first boot.  After that, shutdown, installed Ultra memory chip in mem slot A, rebooted, nothing.  Swapped the chips, rebooted, 1024MB RAM!

Thanks for having this GREAT info available.  It was a litte hard to find, but saved me!

Grateful for the info  dont know why I left the page open but I did.

flashed the bios to a22 on my inspiron 5100 as i couldnt get the f2 to work and got the blank screen came back  to his computer and this  page was still open and tried switching chips  it worked  so still have  the inspiron running but no screen now  but i can access my files thru my network so no worries yet  can access  f2  now and f12 and  just have to wait on the part to replace my backlight to have a screen again