Hi VileLabyrinth

Welcome to H-kon.net
You do not need to upgrade the BIOS if you are going to install additional memory. As far as i can tell, there is one bios update available for your computer that adds some more cpu's to the supported list.
You should see what version you have if you press the "tab" button on your keyboard when you see the dell logo when starting your computer, in your case is should list "A00". The most recent version is A01.
Any idea how much memory you have now? Dell says your computer supports up to 1GB of memory in two times 512MB modules. You can find out by right-clicking on My Computer and selecting "Properties".
Here is the BIOS information for your computer:
http://support.dell.com/support/downloads/download.aspx?c=us&cs=28&l=en&s=dfb&releaseid=R115123&SystemID=DIM_CEL_1100&servicetag=&os=WW1&osl=en&deviceid=308&devlib=0&typecnt=0&vercnt=2&catid=-1&impid=-1&formatcnt=1&libid=1&fileid=151804#2WinRun the BIOS update utility from Windows environment
1. Double click the Icon on your desktop labeled DE051A01.EXE.
The Dell BIOS Flash window appears
2. Click the Continue button.
The message Pressing OK will close all applications, shut down Windows, Flash the BIOS, then reboot. appears.
3. Click the OK button.
The system will restart and the BIOS Flash will be completed.