The loading will get to the point where you click to continue [Mission Splash screen] once you click, the screen goes blank and you hear what sounds like an explosion then nothing. Only a black screen.
I found a solution in the relic forums
Fix for this issue:
Go to this folder:
My documents\My Games\Company of Heroes\Savegames\RelicCOH\Campaigns\cxp2\
Find the file
“oosterbeek_crossing – counterattack.cohsav”
Move this file out of the folder and onto your desktop or delete it.
Run the game, hit continue campaign.
NOTE: This worked for me