I finally had some free time to look into this further. Download Android SDK and extract to a folder on your PC. Go to the Environmental Variables window on your PC, in the System Variables pane, scroll down to Path. Double click on it to edit it. Scroll all the way to the right side of the value, and add ";c:\android\tools" (or the absolute path to your tools folder).
Open a cmd prompt window and type
adb shell remount rw
This will temporarily give you access to the system folder on your phone untill next reboot.
adb push <application_name>.apk or file /system/? folder
Make sure that you're in the folder (on the PC) that contains the app/files you wish to install and move to your phone.