Dell Inspiron 1750 :: Can Work Without Battery?

I have a Dell Inspiron 1750 laptop and it's 2 yrs old now.

For about 6 months, it was saying that my battery was reaching the end of its usable life and I needed to replace it. However, it still worked fine, I just had to keep it plugged in.

One night though, I realised when I turned it on that the message changed from that, and instead it just said "You need to replace your battery". It didn't shut down in my face or anything the same time though, I coninued to use it and when I was done I just shut it down as usual.

The next day when I tried to turn on my laptop, it wouldn't come on. I assumed that this was because the battery died, but my dad told me that if I removed the battery and plugged in the adapter it should still be able to work fine. I did try this, but it still didn't come on.

What I would like to know is if the problem is just the dead battery, or if something else is wrong... someone told me that it could be a problem with the motherboard...

I know for sure that all laptops don't work without the battery, are dell laptops like that too?