Identifying ICs on a PCB
These are most likely a microcontroller, a voltage regulator and three full-bridge amplifiers. 

First thing to check is connectors, loose cables, and on a cheap PCB base material as this, broken eyelets and traces.

The voltage regulator near the battery input is sure a standard IC, find its number and then the datasheet, then check if there is the advertized output voltage when the battery is connected.

Last thing to check is the crystal. Does the µC has a clock? For that, you need an oscilloscope and a 1:10 probe (or simply hold an 1:1 probe near the crystal pins). You should see an oscillation. If not, or only unreliably, the crystal may be subtly broken due to mechanical shock. It's not unusual for toys.

If all that works but the device doesn't, I would give up. No sense in putting more research into that cheap thing.

(I doubt one of the bridge amplifiers is broken, because then, you simply couldn't move backwards or forwards or steer, but the other function would work.)