1) Well EnableClientScript is false, so you're going to be going back to the server to validate. You should remove that (unless you want to postback...) http://msdn.microsoft.com/en-us/library/system.web.ui.webcontrols.validationsummary.enableclientscript%28VS.80%29.aspx
2) Try setting a ValidationGroup on the TextBoxes, the RequiredFieldValidators, and the submit button....it'll link them all together.
3) If you need to validate on the serverside, use a CustomValidator link
. It'll allow you to stop your click events from running if your page isnt in a Valid State. Useful for scenarios where a user has typed in some text which passes the "RequiredValidator", but needs some extra validation.
Give those a go :)