Running a TC hangs on "Define Record Details"

If there is only one testcase having the issue, usually it is hard to pinpoint what's wrong.
You may want to check
1) whether it is browser related(try other browser) which is very rare
2) if there is anything in qm.log at the time when you run the testcase
3) if nothing in the server log file, try firebug and see if there is any clue:
http://www-01.ibm.com/support/docview.wss?uid=swg21657804
4) check with the history of this testcase and see if there is any add/delete activity which could contribute to the behavior
5) go to the sections and see if there is any links(link to the requirement, link to the script and TCERs) in which the original artifacts were removed but it is still in the testcase

There are two things you can try to workaround the issue:
1) create a new TCER and add this testcase in. Run TCER directly instead of the testcase
2) try to duplicate the testcase and then run the duplicated testcase and see if there is any problem. if it works, delete the original one and rename the duplicated testcase to the original name.