In order to displace something, the new thing has to be all that the old thing was and then some more (some more crucial features not just some more sugar). And then it has to be cheaper to top it. Until you can satisfy both requirements, trying to get someone to upgrade is probably going to be an uphill battle.
If a company invested a non trivial amount of effort into creating a web enabled system that was dependent on IE 6, it will likely continue to be used until it becomes nearly impossible to get IE 6 to run on newer computers. Can you guarantee that the new system will do something the old system could not do? If you cannot, then it is probably going to be cheaper at any given moment to fix / replace the few older computers that break down then to reimplement the entire system.