Yeah, that sounds like fun. :-)
Make a file named PlayRandom.bat and paste the following script into it.
CD /D %~dp0
For /F "tokens=*" %%f In ('Dir /A-D /B *.txt') Do (Set /A Count=!Count!+1)
Set /A Skip=%Random%%%%Count%
If %Skip%==0 (Set Skip=) Else (Set Skip=skip=%Skip%)
For /F "%Skip% tokens=*" %%f In ('Dir /A-D /B *.txt') Do (If "!RandomFile!"=="" Set RandomFile=%%f)
*.txt in each
For line to whatever file extension your movies use. You can write multiple extensions separated by spaces, for example
*.mpg *.avi *.divx
Start line will open the file in the default program. You may want to change this to run your movie player, such as:
"C:\Program Files\MPC-HC\MPC-HC.exe" "%RandomFile%"