Blackadder,
An easier way may well be to copy the contents of C
Program Files\ICQ\DB to a floppy and then paste it into the same location on the new PC. The DB sub-directotry usually contains two files and depending on the number of contacts you have and the message history, it may or may not fit.
Depending on the version of ICQ you might need to run the database converter but that's automated anyway once you start it.
It's always an idea to save these two files elsewhere, as it's a royalpain to find and add your contacts - and wait for the inevitbale authorisation to add them!
Good luck.