On my end, I used Resource Monitor to see which application was still listening to port 5037 after all the Eclipse and adb restart were unsuccessful for me.
Start > All Programs > Accessories > System Tools >
Resource Monitor > Network > Listening Ports
This eventually showed that java.exe was listening to port 5037, hence, preventing adb from doing so. I killed java.exe, immediately start adb (with adb start-server) and received a confirmation that adb was able to start:
android-sdks\platform-tools>adb start-server
* daemon not running. starting it now on port 5037 *
* daemon started successfully *