Is it the battery or the adapter?

Please excuse my total techy ignorance but was wondering if I could get some help.

I've a Latitude D510 and for ages it wouldn't work unless the charger was plugged in. The battery light on the laptop would alternately flash green then orange.

Now the computer won't come on whether it's plugged in or not. Has anyone ever experienced this problem? Was going to buy a new charger but I'm wonder if I need a new battery as well.

Also, I browsed the Dell website and the adapters are all different Watts. What difference does this make?

thanks a mil,
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you should be able to run a laptop with a charger and no battery...

why i dont bother with a bigger cell battery is that they seem to like to die out a lot and i'm used to always keeping my laptop plugged in all the time.

but that's crazy me, carrying around a 13lbs lappy...