If by lag, you mean low FPS on those games, Then it is weird. I'm sure that PSU is enough to power your components. Try reinstalling the driver. Did you have a different video card before that? If so, you must have uninstalled the older drivers first.
GTA4 is horribly ported and runs like crap on all but the most powerful quad core systems (really, dual cores are not good enough). batman uses PhysX which destroys performance for some extra superfluous effects.
the other games should run fine. the gtx260 isn't that good a card, but its no slouch. what sort of framerates do you get in those other games?
Technically, a 2.5GHz dual core CPU should be enough to have playable FPS at 1152x864 with a GTX 260. It makes me wonder why it shouldn't be enough. I can disable 2 cores of my i5 750 and still get good framerates.
I have no idea as to what could be bottlenecking the GPU, unless the GPU itself is faulty.
The HeC power supply he has may be the hec HEC500TEWX or the hec Raptor500 500W.
The hec Raptor500 500W can output only 32a or 384ws of power on the 12v rails, which is quite frankly low for a 500w PSU which should have around 40a~.
The HEC500TEWX can only output 37a, out of a specified 20a/25a 12v rail. Odd.
Both are considered low-gaming quality power supplies, and the 1 year warranty should be evident enough of this. I have reason to believe the PSU may be the culprit.
Specifications for a 260 216 core stock clock GPU:
Minimum of a 500 Watt power supply.
(Minimum recommended power supply with +12 Volt current rating of 36 Amp Amps.)
Two available 6-pin Molex hard drive power dongles
As you can see only the hec HEC500TEWX psu meets that requirement (however is doubtful it can perform at that type of amperage without melting down.
I'm with AsAnAtheist, nowadays there is no reason to hold back on upgrading the power supply. They have lots of cheap prices on great power supplies around 600watt-ish upwards to 1000watts. Any of those should have adequate amps to run the hardware.
I would also ask about how big is your case. Sometimes if you have a lot of hardware and no breathing room it can cause video drivers to pop in and out of consciousness. I used to run my GTX280 2xSLI in a mid-tower sized gaming case, and it took me months to realize that my problem with the nvidia drivers were actually caused by overheating.
But remember, you can't have a good computer with a bad powersupply.
cpu phenom2 quad 920 gpu nivida gtx 260 psu ocz 600 watt combine current for 12v rails are 72A. I played new batman game works flawless. i recommend you to change the psu. i dunt know specific about your card but mine requires at least 525 W 38A or more combine current at 12v rails. i dout know well about your power supply and graphics. Check the specification before do anything people cannot juss tell you to do something they dunt know much about your situation check it for yourself. if psu is underpowered then upgrade if psu is enough then call your graphics card tech serivce good luck