How do I update firmware on extreme

Question

I have an old 2nd generation Airport Extreme that my wife picked up at a garage sale for me.  When I try and set it up with my MBP, it gives me a message
That link provides no real help as it takes me to the top level of airport support.  I installed an older version of Airport Utility (5.5) on my Windows PC in an effort to hook up the Airport Extreme.  That worked, as the older Airport Utility was willing to communicate with the older firmware (7.2) on the Airport Extreme.  So its setup and working, but now I want to update the firmware on the Airport Extreme and I can't figure out how to do it.  Like I said, my MBP won't talk to it and directs me to the link in the image above.  On my Windows PC it asks me to point to the firmware I want to update to.  Makes sense, but the Apple website does not seem to let you download the firmware directly.  But pages like this (http://support.apple.com/kb/HT1218) imply the only way to update firmware is via the "Update" button in Airport Utility.  This seems like a major chicken and egg problem.  I need to update firmware, but my MBP won't talk to it until I update it.  And my Windows PC wants to download the firmware onto my hard drive, but that doesn't seem possible.

Answer 1

Bob, you are the man!  If I could buy you a drink I would.  You pointed me in the right direction and I think I finally got it to work.  I'm going to document this with pictures for posterity sake, and hopefully to save any other poor sap that has to do the update via a PC.
On my Windows PC, running the old 5.5.3 version of Airport Utility. 
1.  Clicked on 'File' in the upper left hand corner of the app, then selected "Check For Updates...".  Note I did not click Alt or Ctrl or any of the suggestions you made.  Just a straight forward left-mouse click.
2. That brought me to an update screen for the Airport Utility itself.  I didn't want to update Airport Utility, so I selected 'Cancel'
3.  After hitting Cancel, I got the following two screens.  The first told me there were updates available for my devices.  On that window I selected the "Show Details" button.  That brought me to a screen showing all of my devices and the firmware that was available for them.  I selected my Airport Extreme and hit the Download button.
4.  That downloaded the firmware for me.  The next thing it asked me is if I wanted to update the device to the new firmware.  I hit "Update", but it failed immediately.  No worries though, back at the main Airport Utility window, I clicked on 'Version' again next to 7.2.  Now I get a window similar to what you posted earlier.  Previously my only option was "Other", now I have the option of 7.6.2.
5.  Click OK on the screen from above and after about 5 mins, this is what I see:
BOOM!!! Bob is the man!!!!