Ryan,
A number of valid points have been presented here, certainly the possible damage to your hard drive due to vibration and altitude are two of them. Also consider the possible effect of the non-aviation electronics on the aircraft systems. It is likely that the signals which ARE emitted from the computer won't interfere with the aircraft systems, but how do you know?
I suggest using a more suitable camera, properly attached, for this purpose.
If I were asked to approve such an installation, these are questions I would be asking myself about the "installation":
Does the modification.....
[ alter] A containment or restraint system intended for occupants or the storage of items of mass (e.g. cargo)?
...Affect the flight-crew's visibility or their ability to control the aircraft?
...Affect a communication system required by the approved type design?
...Affect instruments, or indicators that are installed as part of a system required by the approved type design?
If you answer "yes" to any, it's technically a major modification, requiring an approval...
Approach these impromptu modifications with caution, you are taking the responsibility for a modification and validity of the C of A, as well as the safety of the flight....