I am on the same boat here.  My problem I believe is just that there appear a unknown device in the device manager, it has something to do with the power options.  I wish I had updated the BIOS before I did the upgrade.

Please let us know if you find a way to upgrade the BIOS.

Temporarily install a floppy drive to flash the bios.

You can convert the floppy diskette to bootable CD, but still requires a PC with a floppy to make it.

Turn All Of Your Old Bootable Floppies Into Bootable CD's [the easy way]

    First Of All You Need A Cd-Burner, Nero Burning Rom v5.5 or higher
    A Floppie Drive, A Blank CDR Disk
    When You Have Everything: 

Load Up Nero With Your Floppy In The Drive And Blank Cd In The Cd-Recorder
Close The Wizard
Hold Ctrl + N
Until A Box Appears
Scroll Down The List Until You Reach CDROM (Boot)
Click It
Bootable Logical Drive Must Be A":"
Click The Burn TAB
Click New
Click File- add files from A:
Then Write CD
 
Done

Or download the dell exe file to the root of the C drive, boot from the W7 or Vista DVD, get to the command prompt and run the exe from there.

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Unless Dell releases a BIOS update that can be installed from a floppy, that method doesn't work.  The only BIOS update they've released for the Inspiron 531 is a Windows-environment EXE.

As for my issue, the problems went far deeper than needing a BIOS update.  The board was shot.  So I had to replace the mobo (and thus the case) and CPU.  So my Dell isn't even really a Dell anymore.

My bad, I looked up the 530.

You cannot put a Dell bios on a non Dell board.