Your suspicions ar very likely correct. A 235 wat power supply is very small indeed. You should look for a 300 - 350 wat power supply.
They are relatively inexpensive at around £25.
I had the very same problem myself untill I replaced my power supply. Even in the unlikely event that it isn't the power supply in your case, you are certainly going to have some problems if you add more hardware to your system in the future.