I have my account tied to 4 different computers. I can only access one at at time, but steam has never given me that issue. The only thing I can think of is, the last computer you used, steam thinks that it is still being used, ie computer crashed and did not close steam properly.
If this is the case, steam (after a great length of time) should be able to varify if your "old" account is no longer accessing their servers. Only going to steam though will resolve the problem.