Like I said, upgrade. I'm not saying it to be trite, either...this is a major issue your company is going to have. Either they upgrade or they pay the price later on when something happens, because chances are whoever's using that tower isn't too tech savvy.
You're right, though...IE7 doesn't support inline-block. As a workaround, you could install Chrome on that machine and have a shortcut to that page open up in Chrome from the desktop. It's not a perfect solution, but it's about all I can come up with.
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