Hello. Does anyone has the problem with Doom 3 persisting to be at lowest possible resolution? What are the solutions to the problem?

You can set a custom resolution by creating a blank text file in <game folder>\base, renaming it to 'autoexec.cfg', and putting in:

seta r_customWidth 1920
seta r_customHeight 1080
seta r_mode -1
seta r_aspectRatio 1

Substitute the height and width numbers with whatever resolution you want to run at. Widescreen values will cause the HUD to stretch, but it will stop the game from running at a low resolution.

I recommend checking out the PCGamingWiki page for any other tweaks you might like.