Stav,
I'm no expert, but it seems to me that any of the following might have happened.
Gutters. if they are fitted, may have becoome blocked.
Polycarbonate roof panels may have cracked, or their seals may have failed.
Seals/mastic between canservatory and 'existing' may have failed.
Much of this could have been caused by movement..which might also explain 'sticky' windows and doors, but it might also point to previous lack of maintenance.
There are any number of Conservatory Repair/Maintenance Co's out there. Maybe try to find a decent