Will the sims 3 work on this laptop. Intel Pentium dual core t4300 processor. 2.10ghz processor speed. 4gb ddr2 ram. 17.3in screen size 1600 x 900 resolution?

If you use Windows XP, yes. If you use vista, you may have to buy a 2.4ghz processor, at least.

Also, you need 7.8gb of free hard drive space, and one of the following video cards:

NVIDIA GeForce series FX 5900, FX 5950
6200, 6500, 6600, 6800
7200, 7300, 7600, 7800, 7900, 7950
8400, 8500, 8600, 8800
9300, 9400, 9500, 9600, 9800
G100, GT 120, GT 130, GTS 150
GTS 250, GTX 260, GTX 280, GTX 285, GTX 295

ATI Radeon™ series 9500, 9600, 9800
X300, X600, X700, X800, X850
X1300, X1600, X1800, X1900, X1950
2400, 2600, 2900
3450, 3650, 3850, 3870
4850, 4870

Intel® Graphics Media Accelerator (GMA) GMA 3-Series, GMA 4-Series