.ajax submit searching inner html of returned value

.ajax submit searching inner html of returned value

how would you go about creating a var to search the inner html of a return looking for the boolean value of a "successflag" with something such as this returned? I would then base my "success" or "error" function based on what is returned, what Im trying isn't working. 
<HTML>
      <BODY>
            <TABLE border='1'>
                  <TR>
                        <TD><b>Field Name</b></TD>
                        <TD><b>Field Value</b></TD>
                  </TR>
                  <TR>
                        <TD>SuccessFlag</TD>
                        <TD>False</TD>
                  </TR>
                  <TR>
                        <TD>ResponseMessage</TD>
                        <TD>Password could not be changed.</TD>
                  </TR>
            </TABLE>
      </BODY>
</HTML>