What shortcut are you trying to use? Generally shift-t will just do an uppercase T. The only shortcut I use regularly involving the t key is command-t which is new tab in safari/firefox. Is that what you mean or can you elaborate?
I agree. Updating software sounds like a good starting point. If it's a hardware problem I won't be much help but I'm sure somebody else can help you here. Post back if that works. What type of system are you on as well? That could help you find the solution? Computer? OS? Etc.?
Oh, forgot to say i have a MacBook (so no other keyboard), about 4 years old, running SL and up to date. I followed some advice and booted from the instal disc and the problem still existed, so I presume it's a hardware problem. Now shift-t and shift-i won't play. there were a few others but they're behaving now.