If I understand you correctly, you now have 2 devices attached to your PC, the HP Scanjet 4850 and the Cannon iP 3600. Firstly, I'm pretty certain that the HP solution centre only works with the Scanjet and will be not help with any other printer. Also, I THINK that the scan to print function on the 4850 only works within the one device. The only thing I can suggest if thius is correct would be to scan to a file and then print the file to the 3600.
However, I'm also concerned about your PC asking you to install the driver. Have installed your new driver correctly - and have you accidentally, affected/deleted the 4850 driver?