Are there any codes in the Powertrain Control Module (engine computer)? Has the check engine light ever illuminated? From your description it sounds like the exhaust may be restricted by a clogged catalytic converter. If the converter has failed, it would be due to some other component like an oxygen sensor (which would likely set a code) or the secondary air pump which is supposed to pump air into the cat to help the cat burn off emissions more efficiently. There have been some failures of the secondary air pumps due to water intrusion.

The other thing that may be at fault is the computer itself, although it is less likely. Further diagnosis would be required. The diagnosis would be much more focused if a scantool could be used to determine what data the computer is receiving from its sensors. Also there may be some codes logged in the computer memory that could help direct the diagnosis.