Try deleting FW's preferences folder on one of the computers. To make it easier for you, maybe pick the computer whose FW doesn't have incomplete files that you want to resume.

Before deleting FW's preferences folder, please read post # 5 of this thread (click on link): Fixes for Limewire when LW isn't operating as it should
**Refers to LW but same goes for FW.

Close FW & make sure that it's properly closed before deleting the prefs folder. Check in Task Manager. If there's a FW process running - end the process.

When using Vista or Windows 7, you'll need to look for your preferences folder in a different place. Try C:\Users\your username\AppData\Roaming\FrostWire
And more info about how to show hidden files & folders, and how to find the preferences folder here LimeWire Pref Folder in Vista and Windows 7
**Refers to LW but same goes for FW

You'll know if you've deleted the preferences folder properly...when you start FW, it will take you through the setup wizard. Also, all of the settings within FW's options will have reverted back to default. If you restart FW & don't have to go through the setup wizard, that means that you haven't deleted the preferences folder properly. In that case, make sure that FW's properly closed & start again.

Once you've deleted the prefs folder & restarted FW, give it a while (up to 15 mins) before deciding that the fix hasn't worked.