I created this HTML:

<form action="test.cgi" method="GET">
        <tr>
                <td bgcolor="white"><img height="1" width="1" src="px.
+gif"></td>
                <td bgcolor="white" colspan="2"><input type="password"
+ name="htmPassword" size="10" class="rtnavinput"></td>
                <td bgcolor="white"><input type=image src="/images/btn
+GoRed.gif" width="15" height="15" border="0"></td>
                <td bgcolor="white"><img height="1" width="1" src="px.
+gif"></td>
        </tr>
</form>
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to see what gets sent. It fetches:

.../test.cgi?htmPassword=&x=8&y=10
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So maybe you need to do something like this:

$mech->set_fields(x => 1, y => 1);
$mech->submit();
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The script probably doesn't attention to the x and y, in which case you could do simply:

$mech->submit();
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(Untested, and I'd never used WWW::Mechanize.)