I just got a new computer and I was wondering if I can connect to the internet using the same dial up networking account as my old computer and if both computers can be online at the same time. I don't think it is possible but if it is can you tell me how?

If you have an ISP you can certainly set up the machine to get yourself onto the Internet. All you need is either the software provided by your ISP or the neccessary information from the ISP to set up your access manually. (Account name/password, dial-in number if dial-up, etc.)

The choices on how you set things up ("Connect with existing account/ISP, modem, ADSL modem, etc) will be presented when you run the "Connect to the Internet" function.

To have both systems on the net simultaneously you will need a router and accompanying software for the router.

Since you're in the 98 forum, I gather that both machines are running 98FE or 98SE.