Hi Dave,
By the sounds of it your system is really borked - that word again, it was one of my late daughter's most used word to describe a SNAFU.
There might be an easy way to improve matters. If you don't already have OS/2MT then grab it from
http://www.os2mt.tk/ install it and let it have a look at your system. It will make a number of recommendations that you can use as a basis for upgrading. I use it to show me what I need to add on a new system, then I use the separate download functions to get what I want (saves having to remember).
When you have gone through the necessary updates - it shows updates and fixes, you should find it possible to run a later version of firefox. I would recommend that you copy your mozprofiles directory, after you have cleared the cache, to another partition if possible, delete it and then let firefox recreate it according to the settings in your config.sys.
If that doesn't fix the problem then we need to look at other possibilities like something strange in your ini files that needs a good going over with cleanini and checkini and maybe xfix if you have xworkplace installed.
My 'network.jar.open-unsafe-type' is set to false - this is with the 3.7a4pre using the nightly tester tools addon to get all the others to work - all 18 of them and they auto update without problems.
ivan