Dell Inspiron 5100 power/battery help needed

[KK]

Have this 5100 laptop here, that I just bought a new battery for. Put the battery in the laptop and let it sit for about 10 hours. I get back tonight and go to turn it on. A screen pops up say that I got a 70Watt ac adapter plugged up and something about the performance of the battery won't charge or something like that, I press a function key to go into bios. go to the power page and the ac adapter shows up as 70 watt. I wiggled the plug coming into the laptop alittle bit and noticed that the 70W would occasionally go to 90 watt. Thought maybe the plug was bad, got my spare adapter, that one I don't know if I ever got it to go to 90W by wiggling it. I'm thinking the jack on the laptop needs replaced. I powered down the laptop now it boot back up, the battery indicator light stays yellow for about 10 secs then goes out. I'm guessing the battery is not charged as bios only said it was 6% when I first got into it, and it was 2% when I exited and tried to reboot.

Also when it was in bios, when it was on 70Watt it said discharging, but when it would briefly swing to 90W, the discharging changed to charging.

Will this or any inspiron run without a battery in it at all, just straight off AC. If so, this one doesn't.

What do y'all think the problem could be. The power jack? I disassembled the whole laptop and took the system board out and the jack looked alright from what I could tell, nothing obvious.

Thanks,

Edit: the reason I bought a new battery was the laptop was flashing the battery light 3 or 4 times yellow then one green. I figured the battery was dead as it was down to about going from full charge to dead in about 15 minutes.