It's not something the individuals in the institution can likely do anything about (firewalls, locked down machines preventing installs etc). is a very costly exercise, so you'll likely find that many similarly sized places have the same situation. Performing an entire refresh of the OS, browers, hardware etc. I am not surprised that hospitals / academic institutions are using IE7. But hey, you're in this situation now so you need to deal with it as you find it.
It strikes me that you probably should have researched your userbase before building the site.
