I have two computers with Windows XP connected through a 8-port LAN Hub which is also connected to my Cable Internet Service Provider. Now my Cable Provider has a Dial-Up system to connect to the internet, which works on LAN, which has a Username and a Password exactly similar to the Dial-Up system to connect to the internet through an internet modem which works on a telephone line. So currently if one of my computer is connected to the internet through my Cable Provider's Dial-Up system the other computer will not connect, obviously!
So my question is that is there any way I can share my internet connection between my computers? That is if I connect one PC to my cable internet so I can share my connection with the other computer at the same time.

Yes. You would enable Internet Connection Sharing on your connection. Your PC can share this connection out to other computers on your home network. What operating system are you using?

Its Windows XP Professional SP3.

Follow the link to Microsoft's guide for Internet Connection Sharing with Windows XP.

How to configure Internet Connection Sharing in Windows XP

Also, check into the purchase of a Cable/DSL router. It is a more secured way of sharing Internet connections and is quite easy to setup. You also do not have to leave the share computer up and running all the time like with ICS. If you have or will get laptops in the house or do not want to run network cables to all of your rooms, you can also purhcase a s router WITH wireless networking. They are typically between $50 and $150.