Laptop not charging

Greetings

I have an old Dell Studio 1555. I want to keep it as a home computer and to upgrade from hdd to ssd, but I think its battery is dead.

I've tried to following steps:

- Removed the power cable and the battery. Hold the power button down for 15-20 seconds and then put the battery and the adapter back in and start the computer.

- Checked the AC adapter for any damage. There's none.

- Reset BIOS.

Findings:

- There's for a blue light on the connector that's connects the AC adapter to the computer after it's plugged in.
However, the laptop led is not constant white. It blinks 4 times a red light, then 1 time white light then again red.

- In BIOS, at AC adapter type I see 90w.

- In Device Manager -> Batteries there is an "unknown device". I've uninstalled everything there, installed again with updated drivers.

- Last month the battery was stuck at 4%. Now, it says "unknown remaining".

- If I use my laptop with the battery installed, my laptop shuts down at boot or randomly. After I turn it again, I get a black screen with the message: Windows saved the current session to disk because the battery reached its
critical level. [...] Continue with system resume. However, my laptop powers on AC adapter alone without the battery installed and everything seems fine.

If my battery is dead, can anyone recommend the best place to buy a new one?
I would appreciate any advice on this matter!

Thanks so much for your time and help!