What I recomend is: (This works to me after many days with errors)
-Make sure that you have downloaded:
- the Lastest SDK Platform from the latest Android version
- Android Suppor Librarie and Repository from EXTRAS
-Redowload the ADT
-Make a security copy of your project.
-You must have the ADT, the workspace and the project that we will import in the same disk (e.g. C:/)
Now delete the app compat and your project.
In eclipse: File > Import > Android existing project > Next > Browse (The folder where you have your ADT)/sdk/extras/android/v7/appcompat > Import > Finish
Now in the eclipse Package Explorer: android-support-v7-appcompat/libs/ Make on the two JARS: Right click > Build Path > Add to Build Path
Right click on libs/ folder > Buil Path > Configure Build Path and check this two JARS > OK
On the upper eclipse bar > Project > Clean
Import your project > File > Import > Browse your project > Finish
Now, Right click on the projectfile and android-support-v7-appcompat > Properties > Android > And select the latest API that appears > OK
Right click on the projectfile > Properties > Android > Add > android-support-v7-appcompat
On the upper eclipse bar > Project > Clean