Sim writes "I would like to know if tempdb has become full and what to do if you cannot truncate the log? I want to understand the process why you cannot truncate it."
You should be able to truncate the log file. Now I've had this happen to me before and basically what had happened was a job had gotten hung and continued to fill up the TempDB Log File. I had to kill the job, then truncate the log file, but as soon as I truncated the log it filled up again due to the job(s) having to roll back. I had to continually truncate the log file until all the jobs had rolled back.
I have had this happen to me, where the log was filling up and I could not truncate it or shrink it because of table corruption in the tempdb. You can't run DBCC CHECKDB in the tempdb because it is in use and you can't put it in Single-User mode.
The only solution ot this I have seen is to restart the server, which clears out the tempdb. Other solutions are welcome :)