when you pass a variable into a selector you have to concatenate it the same way you do with any other string/variable combination
$("input[type='checkbox'][id^='" +claimId +"']")
note there is extra set of single quotes added as well as recent versions of jQuery have been more particular about quoting the values in comparative selectors.. see API docs for selectors
also if using jQuery 1.6 would be better to use the new prop() method to modify "checked"