There is a module for Apache, mod_speling that will match requests and files ignoring case (and will 'correct' for one spelling error, ie a request for mipage.html will match the actual file mypage.html). It is not enabled on x10hosting and I doubt that they would enable it (it would break too many things).
The other way, a bit of a hack, would be to use .htaccess to route all requests through a php file, ie FooBar.html would be sent to normalize.php?f=FooBar.html. normalize.php would then look for the file, ignoring case. Then either issue a redirect or include/output the contents of the file. Lot of work.
Easiest is to just make sure all your files are lowercase. Then people will get used to entering URLs in all lowercase and you won't have a problem.