Do you use a dongle or the cloud for iLOK?
Was the clock correct on the old machine when you last used the iLOK manager and HW.?
Is the clock correct on the new machine?
If iLOK thinks the times between usage are inconsistent, it can (mistakenly) ‘think’ you are trying to tamper with the licences.
Change for daylight savings clock changes between the usage on the two machines could cause the times to appear inconsistent.
From an Internet connect machine, with the current version of iLOK manager, you could try synchronising your iLOK usb with your iLOK account.
Iain