I did something wrong in SDK Manager (probably deleted something) and had similar problem. But none of the above helped.
Tried to run Android SDK Manager, but it didn't load, showing error "Windows Failed to execute Android.bat" (only later I discovered that whole "tools" folder was missiong in installed Android bundle). So Android SDK Manager didn't start (and I think I remember that proper SDK was there installed before).
I also tried to correct issue in project.properties, but no Android version was available at all. Other forums also didn't helped.
Fortunaltely I found solution. So what I did is found my initially downloaded zipped Android bundle "adt-bundle-windows-x86-20131030" and extracted "sdk/tools" folder. Then I copied "tools" folder to my already installed Eclipse path "C:... \adt-bundle-windows-x86-20131030\sdk\" (Eclipse was closed). Started Eclipse, checked Build Path in my project and it was it - everything was back to normal.
Hope this will help to somebody with similar (additional to initial post) problem.