Good Lord, I'll try to shed a bit of light on this topic (pun intended) since there's so much misinformation in this thread.
El Fenix and AndrewR have the basics right. I won't comment on the lens being the limiting factor on a small P&S with a 10 MP camera because, frankly, I don't know the specifics of the lenses and it obviously varies from camera to camera.
With that said, assuming all else is constant, if the size of the sensor stays constant and you increase the sensor's resolution, you end up with a noisier image. This is due to several reasons which include sensor noise, amplifier noise, the nature of light and many more. Since amplifier and sensor noise have only a very weak relation to sensor size, you can assume that they're more or less constant in the event of a photoreceptor size reduction. However, as the photoreceptor size is reduced, the signal it detects is smaller (fewer photons hit each receptor) and so the noise appears larger relative to the signal and you get a noisier picture.
Related to this, the ISO setting on a digital camera will change only the amount of analog amplification of the photoreceptor's signal. Thus when high ISOs are needed (low light) there are few photons that hit the photoreceptor and you have to amplify it a lot. As I said earlier, the noise from the sensor and the amplifier is roughly constant regardless of the input signal. It is therefore entirely possible that the signal is swamped by noise and is completely unusable. Note that in this whole description, nothing about resolution has changed; a 10 MP sensor will be noisier than a 6 MP sensor of the same size assuming all else is equal.
To counter this high ISO noise, camera manufacturers add DSP algorithms in camera which attempt to remove the noise and retain only the signal. This is effective only to a certain extent and will often remove detail as well as noise as explained by AndrewR.
Anyhow, the bottom line is that higher resolution sensors are generally noisier although there are some techniques which attempt to get around it (for example, using 4 actual photo-sensors and considering them a single super-photoreceptor at very high ISO settings, which produces an image with 1/4 the sensor resolution but with less noise).
As an aside, AndrewR, I believe you are right that RAW images relate the sensor data directly without any post processing at all. Heck, RAW image haven't even gone through demosaicking!