I have been having the same problem, although I did not try to connect with the cable and did not realize it had something to do with the wireless connection. What I did realize, though, was that aMule kept on working perfectly while on my computer no other program seemed to be able to access the internet.
Still, the solution is to lower the maximum number of connections in the aMule configuration -- "Max Connections" under "Preferences". Looking at the statistics I saw that "Peak Connections" was 169, and that "Average Connections" was around 140. Therefore, I set the Max Connections parameter to 120, and now the other programs can access the internet while aMule is open.
I still have done enough tests to see how this affects the performance of aMule.