Had this issue and fixed it today , not sure if it will help you but just like you when i clicked play in steam to launch APB nothing happen , did uninstall and install and every thing nothing worked. What i did today to fix my issue was go to APB on steam > right click > click properties > click the Local files tab > Click browse local files > Double click on TPI folder to open it > Double click on VC2012_Redist to open it > Double click vcredist_x86 to run it you will get 3 options , Click repair and let it do it's thing. After i let it repair i clicked play on Steam for APB and it launched with no issue , did not even restart my PC so hope this helps you and other's.
