In the Python console run the following:
See if your PYTHONPATH entry is listed. I'm guessing not, since that environment variable is probably not available to QGIS's running Python.
To add your scripts folder to console's sys.path do a regular append():
Then you should be able to import your modules from there for that console session. I recommend expanding the ~ to your user's full home path (not sure if Python does ~ expansion).
EDIT: ~ expansion doesn't seem to be supported by sys.path (on Mac, at least).
QGIS's Python console is created by a Python module, 'console.py'. So, if you want to add your custom path to its sys.path in a more permanent fashion, edit the console.py file and add the sys.path.append('path/to/my/scripts') statement after the module imports section.
console.py is located here (for Mac, using KyngChaos.com QGIS package):
Of course, this is a hack that will be erased and have to be redone on a QGIS.app update.
Any adjustment to the running QGIS Python interpreter's sys.path is available to other plugins as well.
A safer alternative might be to make a simple, development PyQGIS plugin that loads and merely does the sys.path.append(), whenever you want it. It could also remove that path from sys.path on plugin unload(). I have not tested whether the sys.path adjustment of such a plugin would be available in an already-loaded console (I'm guessing, it would be.)