If it has gone brown it is not worth wasting a film on. Admittedly I have never used it for many years, but the only developer I know for certain that works when it has discoloured is Rodinal as you mentioned. If you really wanted to try it do a 'clip' test, a short piece of film with a 3-4 exposures on it and see what you get. If it works -fine, if it doesn't then get rid of the bottle.
I used tmax rs developer,an unopen bottle,that was 10 years out of date-it worked as new.T-max developer is different,but it is worth trying before dumping.
I have a bottle over a year out of date that was opened nearly two years ago. Last I tried it worked fine. I'll be testing in the next couple of weeks (have a fresh bottle too) but probably not in time to help much.
Just a warning. Tmax developer is not guaranteed to be dark when it's dead. I had a few bottles a few decades old (from 1980's or so). The developer was clear as new, but completely dead, as in water. Do a test run and see for yourself. If it is less than 15 years old, it's probably good as new