Although <input> ignores the rows attribute, you can take advantage of the fact that <textarea> doesn't have to be inside <form> tags, but can still be a part of a form by referencing the form's id:
<form method="get" id="testformid">
<input type="submit" />
</form>
<textarea form ="testformid" name="taname" id="taid" cols="35" wrap="soft"></textarea>
Of course, <textarea> now appears below "submit" button, but maybe you'll find a way to reposition it.