yeah i do .. i tried all possible ways, but it always says the key is invalid

Doom 3 is open-source. So, there are source ports for it, and they don't include the CD key check. They just require you to own a copy of the game. The websites for these ports will tell you which game files you'll need for the port and how to get it running.

I ended up using one called "Dhewm3" (after about half an hour of testing, there were a small number of visual glitches - flickering weapon/monster models during a few moments - and one crash to desktop, but it... mostly... ran as well as I remember the game running back in the mid-2000s :) ).

Somehow I missed the instructions on here about how to find the key. Still, if you're having problems with it, then source ports are an option.

@anyone: If the serial keys in your account (under the "More" dropdown for Doom 3) don't work, all I can suggest is contacting Support. (You'll have to deal with the bot first but eventually you should be able to contact a person if the bot doesn't help.)

This is what GOG support said

Hello again,

- Please visit our website - > https://www.gog.com
- Log-in
- Move mouse cursor on your username
- Select Games
- Select Doom 3
- Press more - > Serial Keys

This is what GOG support told me and it worked

Hello again,

- Please visit our website - > https://www.gog.com
- Log-in
- Move mouse cursor on your username
- Select Games
- Select Doom 3
- Press more - > Serial Keys