iTunes authorization problem -- that's bigger

Mac 2009 with 2.66 GHz Intel Core 2 Duo and 10.9.5

Recently changed from the latest back to Maverick

now won't let me play lots of iTunes stuff I bought: This computer is not authorized:

It says enter PW. I do. it says it isn't correct. i change password after several times it says it isn't correct. It says change password. i do. Nothing changes except me.

To me the more important question is that it won't authorize this Mavericks computer when it (the same computer) is one of only 2.

This seems to entangle the earlier Apple problem I had with two addresses and subsequent passwords. Help!