no, it's not the battery.
1. It could be the power cord.. Does the power block still heat up a little when you leave it plugged in for a while? You can try getting someone else's power cord (make sure it has the same wattage, amperage, voltage and connector!!!)
2. Could be the power switch. Try pushing it from different angles or something, see if it's broken.
3. Smell around, especially the vents and the power block, see if you can smell any electrical burn.
4. Try pushing and holding down the power switch for 5 seconds.
If all fails, you can always take out the hard drive (should have instructions on how to dismatle it with the dell packaging) and plug it into a friend's computer, or your desktop if you have one to retrieve your notes.
Let me know what works.