EDIT: I even think of attending university majoring in electrical engineering, but I think it's overkill (I'm a BCompSc).
I would just get an arduino and start messing around. While electricity is black magic to me, the programming end of microcontrollers is pretty easy to understand.
If you're a complete noob like me and still have difficulty reading electronics diagram, or sketchy on how transistors work, then get a cheap hackable arduino until you're ready for the more adventurous stuff.
HD video might be out of reach, but you can output to TV (see gameduino). Processing is limited, but you can ship processing to a server via ethernet (see nanode). Storage is limited, but you can have SD card shields (or use a remote server). Or how about radio control (see nanode RF http://http://nanode.eu/)?
Plus an arduino might be a nice companion with a Pi/Beaglebord/Trimslice for remote sensors or remote control. or maybe Lilipad arduino for wearable computing apps.