Easiest thing to do is to use VSS (Source Safe), provided you have a copy of it and the two machines are networked together. If both of these are true, then startup source safe, create a new VSS database on either machine, load the project into the database. Then, go to second machine, start VSS and attach to database created above, then download the project and have VSS recreate all paths needed for the project.
If you do not have a copy of VSS, have you tried recreating the exact path/file structure on the second machine.
If neither above will work for you, copy all the forms and modules/classes to the new machine, create a NEW project and add all the forms, modules/classes, etc. into the new project - don't forget to set the project references (you can use the other machine to locate all the needed references). This is the painful but foolproof way to get it to work - in the process, you may find an outdated or missing DLL/OCX/OLB...