OK. So it doesn't start at all. That is very weird.
Assuming that you have downloaded the latest maintenance build and still encounter the same problem, I would suggest removing soapui.key and soapui.dat from the .soapui directory in your home directory. Or even better, rename them to something else or move them somewhere, that way they don't get lost.
I don't know what could possibly make it not start just because it doesn't have a valid license, it should tell you that you don't have a license and ask if you want to install one. A word of warning though, deleting the two files will forever remove that license (which should be ok in your case but maybe not for others finding this thread on google).
If it isn't directly related to the expired license but caused by something becoming corrupt at the time when the product stopped because the license expired (or something), I would start by looking in the .readyapi/logs/ directory to see if there are any errors logged during startup. It could be that it hangs because of a corrupted settings file, corrupted workspace or something else. It shouldn't but it is where I would start looking. When customer care gets back to you (or you contact them), the log files will probably help them help you.
I am in no position to tell you why you have not gotten a response but I am sure they will come back to you, I am just trying to help you on my spare time while you are waiting. As an employee I can only say I am sorry you haven't got the response you expected.
