Dont assume your battery is working properly even just bought that recently/ A dead battery not really a bad one it just lost the charging system. Try check your battery if it is good, turn on your doom lights and start your car, if your doom light didnt go dim then probably its good. If your doom light goes out or it dim, your battery charging system is low. Recharge it before use.
If all this are fail to solve your problem, check your battery connection for corrosion in the terminal and the cable connector, clean it and tighten all the bolts. If this still wont work then remove your starter to have your solenoid check this causing starter will not cranked or not a click sounds because your solenoid is bad.. This the most common problem of a car involving no current. Remember that this is electrical not mechanical so your problem is mostly dealing with ignition (DC)system. Kapag hindi parin masagot yong problema eh......palit nalang ng kotse. Joke lang .