For $300 or less you are not going to get a laptop that can play games decently. In that range you are probably going to find laptops with the AMD E series (E, E1, E2) APUs or Intel Celeron N / Pentium N series CPUs. They have pretty weak processing power (especially AMD) and they also have pretty weak graphic cores. They are generally good enough to watch videos with. Playing very simple games is possible, but I don't think you will see better than 25 frames per second on the lowest settings. DOTA 2 uses Valve's Source Engine which has pretty low requirements so I am guessing you can play it. But for games that do not have very low requirements, they are likely to be unplayable for most people.
I recommend you look for laptops with the A8-6410 APU since at least it is more powerful than the CPUs I mentioned, but those laptops probably start at about $350 like the following Toshiba Satellite that is on clearance sale at Best Buy. Performance is still low rather low though.