I have 2 identical Inspiron 1300 laptops with the identical problem. They are my kids and are in excellent condition for their age but kids being kids they both had to be formatted and xp re-installed. Ever since doing this on them both my bios shows no battery and then also the same in xp on the power settings. Cable plugged in and no battery installed. None of them will run without the power cable as the laptop thinks it is not even plugged in. I dont live with the kids but my ex-gf tells me they never had any charging problems only prior to this, only viruses and malware rubbish. As you can imagine she is now having a moan at me for busting them rather than fixing them lol!
I am hoping there is an easy solution to this or is it just possible the pair of batteries have failed at the same time LOL!
It's curious that two laptops have failed at the same time but pretty unlikely to be a software problem, so deny all responsibility.
This has happened with other Dell laptops including mine -- probably a failure in the power supply circuitry on board so that the battery just isn't being charged. You can test this if you can find another Dell that takes the same type of battery. Charge it in that and you'll probably see the charge registers in the BIOS of yours and the machine will run on the battery -- for a while.