Is my altima in "limp mode"? '95 Altima GXE (Automatic trans) 230,000Miles

My transmission has been acting up when it was cold outside, didn't think much of it, the usual act ups slipping, late shifts, etc.
Well the other day it warmed up a lil, drove the car twice that day, but when I was going home my car went from first to second normally, but it would not go to third... It never did go to third. So I stopped and put it in reverse thinking it might help to back up a bit, shut the car off, turned it back on, took off and it still wouldn't go to third. So today I drove it again, but it still wouldn't go to third. The transmission is old and never been serviced. I was planning on replacing it anyways.

My question is... is it most likely the transmission, or something like a shift soleniod? My dad said that since it won't go to third that it is in "limp mode" and will only go so far until it quits working. I figured if it went to limp mode or whatever, the check engine light would come on or something.

If it is in Limp mode, how long/far will it last? I already drove it about 25 miles since it started doing this.

 

Nevermind... driving it this morning and the O/D Off light kept flashing real fast and then the car died. Turned it back on got a little further and it did the same thing. Calling around for a used transmission today. Do used transmissions usually come with a torque convertor and shift soleniod?