Battery doesn't charge AND frequent shut down when only on AC power

Question

Hello all,
I've spent some time browsing and searching this forum to avoid asking a question that has already been answered but I haven't seen a complete answer to this situation so here goes.
I have a Lenovo 3000 N100 model 0768DKU.  Battery (P/N 92P1185) started not charging/not holding a change about 6-8 months ago AND the laptop now abruptly shuts down even when on AC power.  From the forum I found out about the 18 month battery replacement policy but I'm just a few months past the 18 months so out of luck there.  Normally I would just buy a new battery but the last few months I've been getting very frequent shut downs when the laptop is exclusively on AC power even with the battery removed!  This has kept me from buying a battery because the laptop won't stay on even when it's plugged into the wall then how will a battery help? 
This has really thrown me for a loop since the laptop may run 30 minutes then it's dead like you pulled the power cord.  Turn it back on maybe 10 minutes then dead, or 5 minutes then dead repeat over and over.
Steps I've taken since browsing the forums:
Virus scans/spyware are clean
Used compressed air on the fan vent to remove a little dust, opened up and sprayed out dust nothing major.
Speedfan is reporting cpu temperatures of 65C to 69C at 99% idle.
Reseated memory
Questions:
Would a new battery potentially solve this problem?  I'm not sure how since it shuts down even with the battery removed and only the power cord plugged in.
Bad AC adapter?
Thermal problem?  It looks like the cpu is still below temperature ranges based on Intel but it sure seem like a thermal problem to me the way it shuts down.  I'm trying some new thermal grease tonight but not sure if that will realy make a difference.
Any suggestions, I'd hate for it to be motherboard, etc.
Sorry if this was answered elsewhere I've seen all the battery posts but not how the battery would address the fact the laptop shuts down even when on AC power with or without the battery installed. 
Thanks,
Chad 

Answer 1

Hard reset didn't work for me either, thanks for the tip it was worth a shot.
Thermal paste kept temps lower around 45C still suddenly shut off like usual while on AC power.  3, 5, minutes, etc.  Doesn't appear to be thermal.
Could the "bad" battery somehow be messing up the power circuit and cutting off.  Looks like the battery problem with these units is huge wish I'd been looking earlier since I was within the extended 18 month period at the time.  Just want to hear that someone bought a battery and it fixed the problem....