Hello Luc,
Did you transfer your Hauptwerk settings (via 'Backup | Restore ...' in Hauptwerk) to your new PC, and, if so, have you avoided changing the audio routing settings in Hauptwerk since doing so? (If so, then we can assume that your Hauptwerk settings are still as you'd like them to be.)
If so, in Hauptwerk, are you routing the wet+dry mixed audio to the HauptwerkVSTLink's channels 1 and 2, and the wet signal to its channels 3 and 4? In particular, are you doing the wet+dry mixing within Hauptwerk, or trying to do the mixing within Reaper?