How to capture enter key being pressed on pages containing multiple forms?

I have inherited a web application where the usual ability to press return in any of the input fields has been disabled for the very good reason that the page contains multiple forms, and the application would not be able to determine (or, so I am told) which form to action. The application has been designed so there are no submit buttons (as in input type="submit") and, instead, the designers have gone for onclick handling. Here are two buttons that are defined on one of the pages, included for illustration

<input type="button" value="LOGIN"  name="btnLoginOk" onclick="submit(); />"

<input type="button" class="button-click-grey" value="Find Link Partners"  
    onclick="raiseEvent('SubmitForm','',this);" style="cursor:pointer;" />

But I really want to be able to allow users to press return if they wish e.g. if they've just typed into a field associated with the LOGIN, then detect that and action the onclick="submit();"

Perhaps there is a solution with jQuery.