EDIT:
I found something.
The guy at this link Unrecognized Windows Sockets error: 0: JVM_Bind in Flash Builder has a workaround. Problem is you have to do it everytime. He suggests using TCPView to see and close opened connections that are using the same port as the debugger.
People in this thread http://forums.adobe.com/message/653125 also notes that an old version of NOD32 was causing the problem.
ORIGNAL ANSWER :
The second error you get clearly indicate a problem with the Java Virutal Machine (JVM). I don't think it's project related at all.
Try checking out installed JREs (Java runtime environments) in Flash Builder.
Window -> Preferences -> Java - > Installed JREs
Check if there's anything strange here, like unknown JREs. You should use "Adobe Flash Builder 4.6", typically located at "C:\Program Files (x86)\Adobe\Adobe Flash Builder 4.6". If it's not here add it (Add, Next, paste corresponding path) and restart Flash Builder.
If it's already there, you might want to redownload Flex 4.6 SDK and replace your current one (typically located at "C:\Program Files (x86)\Adobe\Adobe Flash Builder 4.6\sdks").
It's unclear if you have uninstalled Flash Builder or not but if that's not the case and the above solutions doesn't work I'd considered reinstalling it from scratch.