Draith

Hello, I'd like to report a problem with my newly obtained refurbished Dell Latitude C640.

I recieved it Christmas Day from my parents when they bought it used/refurbished. I downloaded games, software, antiviruses, etc on it, and I seemed to enjoy it for a while.
..That is, until it powered down on me.
It powered down randomly, even though I had the AC Power connected in the computer. As soon as that happened, I disconnected the power going to the Laptop. I went into another room, plugged the power into a different plug, and the charging light went on for my very weak computer battery (It only has 5 minutes fully charged).
I powered it on and found a message at the very top. Something about the Time being zero'ed or something. And also- "F1 to Continue and F2 for Setup". I thought it was a temporary error, so I just hit F1.
Everything was then okay for at least 3 minutes, until it happened again. My computer's AC Adapter stopped sending power, and it was running on the very weak battery. It then completely shut down after wards.
I replugged the adapter, and the charging light doesn't turn on. I tried to power the computer on but have failed to, until I borrowed another battery from a relative. I put the charged, but weak battery in the computer and powered it on. The same error came up, and I continued on. I scanned for viruses until it powered down because of the battery.
So now I'm pretty much stuck. It looks like I have to replace my CMOS battery... But I'm a little puzzled on the AC Adapter issue.

I hope I get a solution for this problem.
Thank you for your time and support. It is truly appreciated.


Overall Summary:

-Will work on charged battery
-AC Adapter will not work. (It's not faulty either, I tried two different ones.)
-CMOS Battery appears to have died.

Questions:

-Will replacing the CMOS Battery solve my AC Adapter problem?
-Is there more problems than I think there would be?