Windows can not increase the size of your memory, but it can increase the size of your virtual memory. i.e. it is reserving a larger portion of your hard disk to temporarily store stuff that it would have preferred to keep in the memory; but it can't find enough real memory free to use.
It makes the PC slower, but allows it to run. Yes it sounds as if it is "screaming out" for more real memory.
One thing you could check is the number of things you have running at the same time. They all grab a chunk of memory for themselves, and so if something doesn't need to run it may as well be closed down.
Also take a short while to see how much the cost is to upgrade your memory to max before opting for the new PC route. (Check the link I posted ) If the upgrade expense isn't great then it may be worth trying. But of course you do run the risk of still being unsatisfied and ending up buying new on top.