4100 Power Problems (HELP)

First off I’ve seen the many threads about the overheating issues with the 5100. 

My 4100 has similar problems.  I monitor the habits and here is what I’ve come up with so far.

The laptop runs fine with just the battery.  It does not power off unexpectedly at all.  But once I plug in the a/c adapter it will shut down randomly.  When it shuts down I cannot power it back on.  I have to pull the battery out, unplug the a/c adapter and let it sit for a few before I can do anything.  Once it’s sit for a few minutes I can power it back on and use it like normal (without the a/c adapter if the battery is fully charged).  Once the a/c adapter is plugged back in, it will shut down again.

Even when I have the battery out and just the a/c power cord running the laptop it shuts down automatically. 

I’ve cleaned it with compressed air from the vent and fan.  Very little dust came out.  I’ve tried another power cord and it did not correct the problem.  This is a new battery.  What else can be the problem?