Welcome to NICO Chip! If you don't have your FSM (factory service manual) I would download it at http://www.phatg20.net You will need to do a google search for the free software to decompress the .rar file. Then you'll have a full .pdf version. I would suspect a problem with one of the control units, but I don't know much about the I35, so that's kind of a wild guess.
If the fuses burn out pretty quickly, I would start unplugging components (e.g. wiper motor) and see if you can isolate the issue that way.
Do you have any aftermarket accessories installed on your car, especially that have been modified recently? Those are always a good place to look...
Good luck!
Heath
1990 Infiniti Q45 - AKA "Q2"
2005 Infiniti G35 - Sedan A/T FOR SALE
1997 Nissan Truck - XE - 5 Speed M/T