There are several things that need to happen in order for it to launch on both of your PCs. Most importantly, Inner Space needs to be able to connect to the second PC. It uses a different port and different method than ISBoxer uses, so one connecting doesn't necessarily mean the other will immediately work.

The way to troubleshoot this issue is to right click the IS icon and select "Console" -- do this on both PCs. When you launch the Character Set on your main PC, information will be output to this console window, as to what it is trying to do, what happens correctly, and what fails. If it successfully connects to the second PC, then you will see more information in the console on the second PC -- which should point out the exact problem. If it does not, then the failure will be reported on the main PC. Either way, one of the two will tell you what the problem is.

Most commonly it is one of the following:
1. Incoming connections are not enabled on PC 2. Solution: enable incoming connections (right click IS, click Configuration, check the incoming connections box, click Apply, then restart IS)
2. A firewall on PC 2 is blocking incoming TCP port 10101. Solution: unblock the port in your firewall
3. PC 2 was set up by copying the IS folder from PC 1 and therefore the saved "Uplink Name" is the same on both, resulting in a rejection of the connection from PC 1. Solution: change the name in the IS configuration window, click Apply, then restart IS

Whatever it is, this should help you at least find enough information to post back here with more details on the error, if not solve it