I’ve just found out that using JavaScript’s getElementById() function doesn’t quite work as expected when dealing with controls on SharePoint pages. This is because SharePoint uses its own identifiers, so TextBox1 becomes something like ctl00$ctl00$g_3f6d90e4_335b_467c_a53f_6ae00bca6b63$ctl00$TextBox1.
Fortunately there’s a simple solution – instead of the following (which will cause an “Object required” JavaScript error):
document.getElementById("TextBox1");
you need to use this, which will insert the correct full ID for the element and thus work correctly:
document.getElementById("< %=TextBox1.ClientID%>");
It gets a bit more complicated when using nested controls, which is explained in this post by Eric Shupps.