If your batteries are new then the next culprit in line is a dodgy connection somewhere. Do you have a 27 MHz or a 2.4 GHz transmitter? If that is all gobbledegook to you, does it have a telescopic aerial that pulls out to about 3 feet or does it have a stubby plastic bit about 2" long? If 27 Mhz/telescopic aerial, then the radio system is likely to be fairly old, and a good clean of all the plugs and sockets with some WD40 and an old toothbrush might help. Of course, that could be the problem whatever system you have.
Whereabouts are you? Do you know if there is a model boat club near you? I guess from your question that you aren't familiar with RC systems. The type of problem you describe sometimes needs a bit of swapping parts to identify which bit is faulty, but as you don't have spare bits to try, that won't work for you. But if you can find a fellow RC enthusiast you should be able to track down your problem.
Good luck
Greg
