i was able to reproduce the problem you described by downloading the zipped application and running it on my own machine without modifying the proxy. the reason the application functions in firefox and chrome is because those browsers support CORS and can POST without a proxy at all.
it is absolutely essential to make sure you are working with a local proxy (rather than one hosted on arcgis.com). in order to troubleshoot yours, try setting the mustMatch flag to "false" temporarily and testing something similar to the following directly in the browser to see if a page is returned.
http://[machinename]/proxy/proxy.ashx?http://esri.com
see the following article for more information about configuring proxies...
if you're certain that you converted the folder which stores the proxy to an application using IIS manager and you're receiving 500 errors regardless of the page you try and access, its tough to say.
here are some possibilities
1. an outgoing proxy is also in use which restricts access to pages to known identities on the network. (this could explain why you yourself could visit esri.com on a machine, but a request made on behalf of the application pool is denied). in this situation it is possible either that the request is intercepted by the outgoing proxy and blocked, or that it bypasses the outgoing proxy entirely (and still fails)
it would be helpful to get your IT staff involved to try and root out the cause of the problem. tools like wireshark and tcpdump provide the low-level information necessary to snoop appropriate packet traffic, but they aren't particularly easy navigate.
esri.config.defaults.io.proxyUrl = "/proxy/proxy.ashx";