Alienware Sentia (?) laptop not charging

Don't know if this is the correct place to ask this or not -- if it is not, my sincere apologies.

Anyway, a coworker of mine recently picked up an Alienware Sentia (I think) laptop on Ebay to use as a beater-type laptop to use on her camping excursions this summer.

She said the battery would charge all day long, yet the laptop would only get like an hour charge. I figured it was the battery, so she ordered a new one. Though it also looked like the charger was a little beat up, so I told her she probably should get a new charger as well.

So while she is waiting on the new battery to arrive, she tried to run it directly on AC with no battery. It won't work for some reason. I could always run directly from the AC charger on my old Dell's. I don't even see where it looks like the charger is powering the laptop. Can't see any indication of it being on AC power.

Anyone have any idea what the problem could be? Guess she could wait until the new battery arrives to see what happens there. But I always thought one could run it just off the cord(?)

Thoughts?

Thanks!

Joe