This is a very annoying problem indeed.
The ASP-program running on your server produces a webpage with html and possibly javascript code, and that's interpreted by the browser. Browsers can't do much more than that (interpreting html and javascript), except calling addons like flash and mediaplayer and java for all those things they can't do themselves.
Obviously, the html/javascript-code produced by the ASP-code produced by the guy who wrote your current site wasn't kosher. There are difference between IE6 and Firefox and Opera and Safari, and a reasonable requirement for any implementation is that it works on all of these. Details of how it looks might be different, but it should work without errors and look good enough to be presentable. You shouldn't have accepted it back then in the first place as long as it misbehaved on Firefox.
All you can do now is to find out what doesn't work, why it doesn't work and correct it. And you will need somebody (maybe yourself, maybe a professinal developer) with enough knowledge of html, javascript and asp to do it. There should be no need to change the backend (that is, the Access database and the SQL-database). Just the details in the html produced.
It's impossible to say how long this takes before doing it.
Hope this helps.
Kees
My company's website has worked fine on IE6 using W2000. I've just installed Vista Business with IE7 and have discovered several problems. The site was only tested on IE6 and I was aware that it didn't work properly on browsers like Firefox, but didn't have the budget time or expertise to adapt it! It's a 20 page site in two language versions. It was developed in ASP and works with an MS SQL2000 database. I use an Access interface to access data, add comments & update menus etc. The menus when pulled up using an IE7 browser no longer display as when using IE6. In some cases they cut off at the first word eg United instead of United States. In others they don't display the menu selections at all but the category I'd classed these selections in, which shouldn't appear at all! Also I seem to have a problem with caching whereby the usertype isn't recognised. This problem seems to go away once the cache has been cleared.
Does this mean I'll need all my code reviewing to ensure it conforms to IE7 standards, or are there some obvious fixes that are already documented? Does Microsoft provide any practical help? If I'll need to hire a developer for this, is it likely to be a big job what should I expect to pay for such adaptation? I'm only a very small business but dependant upon this website.
Your advice would be much appreciated.

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