remote access rooted device with broken screen
Suggestion 1:


Run an ADB shell in ClockworkMod
Remount /system in readwrite mode.
Add this to /system/build.prop:
persist.service.adb.enable=1
Save the file.


Suggestion 2:

You said that you have installed CyanogenMod. So you probably have a custom recovery, right? You can boot into it, connect your phone to your computer and go to "mounts" -> "mount USB storage".
Then you can access your internal storage.

Suggestion 3:

With a little bit of work you could flash a custom kernel with USB-OTG.
http://forum.xda-developers.com/showthread.php?t=1450298

Please note that you need an external power source (USB-Y cable, powered USB hub; see the link).

Then you can use a mouse and a keyboard to control your phone and access your data.