Does the system correctly identify the AC adapter (F2 at powerup) or is it listed as "unknown"?

It correctly identifies. Just checked, it lists as "AC Adapter Type 90W"

Hello MaddyVoldy,

I would suggest few steps would which would help us in isolating the issue further:

1. Check the Battery Health in the BIOS. To enter BIOS Setup, restart the computer and keep tapping F2 key at the Dell logo screen. Check the battery health and make a note of the message. If anything other than your battery is "performing normally", the battery should be replaced.
2. Dell offers a free Battery Diagnostic test, to run the test refer to the Dell Battery Diagnostics site.
3. Try checking with another battery if available. 

Please try the steps and write back with your findings. 

Hi,

1. Couldn't find the Battery Health option/entry in the BIOS. Looked all around.

2. Ran the Diagnostics, it said Battery Life Test Result: Failed

Hello MaddyVoldy,

Since the Dell Diagnostics on the battery failed, please consider replacing the battery.

**NOTE: The warranty for a Dell battery starts from the date of purchase of the computer. Dell battery has a warranty of 1 year irrespective of the system warranty. In case the laptop is more than 1 year old,  the warranty on the original battery has expired and you would have to purchase the battery. For More details please refer the article on Laptop Battery FAQ's.

You can purchase the battery by contacting our Sales Team # 1-800-357-3355 (US Customer Only).

Please let me know if you have any other queries.