Inspiron 5150 Dead, Amber Battery Charge Light on

After a week and a half, my new Inspiron 5150 is suddenly dead. It worked fine yesterday and I shut it down normally at the end of the day leaving the AC adapter plugged in. Today when trying to start the machine, there was absolutely no signs of life. No noises or lights of any kind. I unplugged the power cable immediately and checked if the machine would start when running from battery. No luck. Then I removed the battery and re-inserted it. Pressed the power button next. The green power light flashed shortly and the amber battery charge is lit constantly. I repeated battery remove/re-insert for a few times and it behaves in the same way every time.

Next I removed the battery and plugged in the power cable. The lights flashed quickly like is normally the case when the cable is plugged in. Pressing power button with the battery removed and the power cable connected gives exactly the same results as in battery operation; power light flashes, battery charge on even when there is no battery inserted.

Two days ago I downloaded and succesfully installed the latest BIOS, A29, which is supposed to fix some battery problem. Not sure if this upgrade is related to my problem in any way and in any case the laptop worked fine for two days after the BIOS upgrade.

I think I will need to call Dell on Monday morning, but is there anything I could try in the meanwhile?

Inspiron 5150 with P4 HT 3.06 GHz
2 x 256 MB of RAM
UXGA
GeForce FX Go5200 64MB
40 MB Hard Drive
Truemobile 1300
NEC DVD+RW Writer 4x
Windows XP Pro