well, you're not stuck with the same RAM unless you're already maxed out, and if you're maxed out and you still don't have enough RAM then yes, it is time to get a new computer. if your machine is way out of date, sure; putting a 1.2ghz processor inside would be overkill -- you'd still be crippled by the rest of the system.
but if your machine is relatively recent, a processor can make a world of difference, for a fraction of the cost of a new system.
just be sure to do your homework before you buy a new processor -- you're better off spending a little more on a well-reviewed manufacturer. some cheaper 3rd party processors are prone to serious issues.
edit: just saw DontHurtMe's post. those two brands are worth looking into, as is Sonnet.