Primary and Secondary DNS for my website

I have an in-house web server which becomes unavailable if my ISP connection fails. Now I have 2 ISPs and want to setup two DNS servers connected to two different ISPs so that they can resolve my website if one of my ISPs is down. I tried setting up these DNS servers using windows 2003 as ns1.mydomain.com and ns2.mydomain.com but if primary server (ns1) is down explorer is still looking for ns1 instead of ns2 and website is not available.

Please advise how to make such an arrangement