I had openGL probs with Medal of Honor MP Demo but not the other Medal of Honor stuff. I have Nvidia card and latest drivers for everything. I even had a fresh install of hard drive. I discovered from Nvidia that Medal of Honor(and other games) gives them grief so they wrote special settings to the driver for Medal of Honor(and other games). Great support nVidia, THANKS. 
You need to open the driver and designate that Medal of Honor runs under their difined settings. Here’s how:
Right click desktop/Properties/settings tab/advanced button/Nvidia tab/performance and monitor (in the small window which pops out to the left)/under application profiles choose your flavor of medal of honor then choose Medal fo Honor under Active profile. If your application is not listed under application, you can add it by clicking the Modify Profile button and the choose browse to select your programs .exe.
This worked for me. You can find these instructions with pictures at nVidia.com: