Just got the app through in IE8.
I rang 001-202-344-3710, spoke to a very friendly customs officer, he advised me to google cbp.gov, then click on esta under Learn More, then click Apply Here (basically the same link as emmt's above), page wouldn't load for me but loaded for the officer. He advised to try another PC as this was sometimes an issue.
So I switched off PC and was planning to try a different PC later, came back just now, tried for the heck of it and it worked - very very strange! There were no setting changes in between.
The officer did say if the issue persisted to ring back and they would help out.
Just thought I'd update in case anyone else came across this issue.