Tell us the Operating Systems that each computer uses. You need to know what the Network name is that the existing computers use. (MSHOME or WORKGROUP?) I assume the works laptop uses a domain name for networking in the office - am I right or does that network have a name as well?
In principle you need to set up a network on the works laptop that`s the same as the home one. Then you should be able to see the other computers and share files etc.