That C2D T9600 CPU is socket P (478pins) and your ASUS UL50vt motherboard is socket BGA956 (956pins).
Other BGA956 CPUs you could consider would be:
C2D SL9600 2.13Ghz / C2D SL9400 1.86Ghz / C2D SL9300 1.6Ghz or SU9600 1.6Ghz.
I can't actually confirm these CPUs would actually work - at least they're the same socket and the electrical specs are 'close'.
Because of the complexity of how the CPU and cooling system are installed this isn't really a DIY job. You're much better off having a factory trained tech do the upgrade for you.
-> To be honest I think you'd better off selling your ASUS UL50vt and then buying a new laptop that has the correct specs you need.