Is there a quick-fix for the Galaxy Nexus when it signals "charging" without beeing connected via USB?
If you are familiar with such things, iFixit has a teardown report for the Galaxy Nexus, it's fairly easy to disassemble it to reach the micro USB port after step 7 and inspect it.

I use isopropyl alcohol and q-tips for cleaning normally.

I'd however not suggest you try it if you have no experience with such stuff.