Hello and welcome to the forums
How is your performance in other games ?
Also,AMD recommends 500W or greater PSU for a 4870 http://www.amd.com/us/products/desktop/graphics/ati-rad...
"500 Watt or greater power supply with two 75W 6-pin PCI Express® power connectors recommended (600 Watt and four 6-pin connectors for ATI CrossFireX™ technology in dual mode)"
GTA4 is a CPU-intensive game and with that resolution, gaming performance will depend more on your CPU capability rather than the GPU. And as Maziar said, 4870 might require more than what your PSU has.
1. Remove drivers and update to the latest driver.
2. The powersupply might be too low for a 4870. You would need 500w and higher.
3. The CPU speed could also be the problem in slowing down loading time. 4870 is a good and GPU and shouldn't have problems playing GTA4.
Theres so many posts about this game, its a leach and just eats everything thats why it wont won its probly the most demanding game for the PC, even more demanding then crysis.
The reason why is because its a console port and is supposed to be played on the console, why do you 99% of pc games dnt need a joypad? Yes you can buy them but it still works out best with mouse and keyboard.
Best fix for you instead of buying a new PC is spend £60 on an Xbox 360.