No, you don't need an internet connection, but make sure Hyperterminal works on the XP and the Win 7 side first. You just want one computer, hyperterminal and Tx connected to Rx. See if it echos.
Then do the same to the other computer.
For the two computer test:
Parity, # of start, #stop bits, Baud and # of data bits must match including handshaking and baud. The wrong characters received means your getting close.
If you want to see what your typing, you will have to enable half duplex or local echo.