Commercial "anti-virus" software is worse than useless on the Mac. If you have any, uninstall it.
Open the Accounts preference pane in System Preferences and check your login items. Are there any you don't recognize? If so, what are they?
Please connect your computer to your router using an Ethernet cable, if you don't already do so. Turn off WiFi/AirPort. Check that the Ethernet connection is working, then boot in safe mode. Log in, but don't launch any applications. Do the files still download?
If not, launch your browser. Do the files download now?
After carrying out these tests, please reboot as usual (not in safe mode) and restore your usual network connection.
Mac OS X: Starting up in Safe Mode