Well personally I would have to say the answer is no, you have no chance of tracking a computer this way.
When a computer first connects to the interent it does allocate something called an IP (interent protocol) address.
This is a string of numbers, sort of like a phone number, an example may be: 192.155.1.101
The problem is that the IP address changes depening on things like which ISP you use and so on.
I would be interested to hear if others think there is a way of doing this, but I do not think it is possible.