Your desktop won't be able to run the game at all, its CPU, RAM and integrated graphics are below the minimum requirements for GTA IV.
As for your laptop, it's hard to say without knowing what graphics it has. Look for your display adapter in the device manager, and post which laptop graphics chipset you have. If you have one of the better ones, you might be able to just barely run the game on the laptop, but it probably won't perform that well. Grand Theft Auto IV is a very poorly coded game, and tends to run poorly on anything less than a quad core. A slower dual core laptop CPU might barely meet the minimum requirements, but it may not give you good performance.
You have fairly weak integrated graphics on the laptop. If the game even runs at all, you probably will not be able to get an acceptable framerate, even at lowest settings at the lowest possible resolution. GTA IV is a very demanding game due to the horrible porting job Rock Star did, it won't run well at all on weak hardware, and even strong hardware can struggle with the game at times. I doubt your Toshiba laptop is upgradeable, only really high end laptops ($1500 and up) have upgradeable graphics, so there isn't much you can do on that front. If there is a demo, download it and try it on the laptop, but odds are your average framerate will probably be something like 15 FPS or less on the lowest possible settings, basically unplayable.
Your options to play the game basically boil down to either build a new desktop that can actually handle the game, buy a laptop with a better graphics card, and preferably better CPU, or buy an XBox 360 or PS3, and get the version appropriate to whichever console you get.
It says right in the name, you have a dual core CPU, not a quad, there aren't a lot of quad core laptop CPUs due to the fact they consume more power and hurt battery life. COD: Black Ops was also not very well ported, but it is easier to run, especially at low settings compared to GTA IV. Like I said, you can try a demo and see how it runs, but I wouldn't hold out much hope. It's highly unlikely you'll be able to squeeze out playable framerates with your laptop. Best case scenario: the game would run, but it would be very, very choppy, maybe you could just barely get 30FPS in a very quiet area, or in the indoor sections. Out in the city, your laptop will choke, even at the lowest possible settings.