I've just receieved my replacement ME2 game because I had problems installing the last one, but now I'm getting the exact same error in the exact same place:
"The installation of Mass Effect 2 has failed. Unable to open a data file."
Am I just having really, really bad luck? I'm worried the suppliers won't replace my game again
It could very well be a failing DVD drive. What is the 'exact same place' that you mentioned? Can you post the filename?
If you have the time, try creating two ISO files from both DVDs and mounting them with a 3rdP application like Daemon Tools or MagicDisc. If you can't create an ISO file due tio the same problem, consider trying a friends drive and see if it installs for them or create the ISO files on their computer then copy them over to yours.