When you get near to running out of ram, the system will use the page file. At that point, it will write the RAM to the hard drive instead.
Windows will then page sections of memory in and out of the RAM/pagefile.
If at any point your hard drive is full (not able to use the pagefile), and your RAM starts filling up, windows will pop up and tell you exactly that.
Your computer is fairly old, the specs are fairly low... If you upgrade to a more current system it will clear up most of your problems.
All in all.... if you ran out of ram you would get a different error. The game would never attempt to write to ram that doesn't exist, that's in the nature of how it was programmed. Your problem lies in that 1. you need to run as admin, 2. your ram is corrupt, or 3. there is something wrong with the game, and it's not compatible with your system setup (which is unlikely).
Your pagefile may also be stored on a corrupt portion of hard drive. Try disk defragment and see if that clears up the problem.
Furthermore, the RAGE engine directly interfaces with the ram, on a system level (system and assembly code), unlike other engines that interface with the ram through windows. GTA:IV was the first game that really pushed RAGE to it's limits, and therefore there are lots of issues with the engine --- as we all know (performance related, etc.)...
Also...
Without the pagefile, on 2gb of ram the game would never get past the loading screen. Once you are in game, around 2gb of ram is being used solely by IV (on top of that you have windows... that's .25gb / .5gb depending on your version). additionally, a minimum of 250mb will be used on your video card.