Basically, in ajax call (from jquery) you should have action variable, i.e.
$.ajax({
type: "POST or GET", //and theese are not the same, use GET for retrieving, POST for new entries
url: "hit/your/connector",
data: { action: "path/to/proccessor" }
})
Regarding access denied, there are two options (quote from docs):
There's a few reasons for this. One is that the connectors are locked down and don't allow anyone without a MODX manager session to access them. Secondly, all requests to connectors must pass a unique-to-your-site authorization key that prevents CRSF attacks. It can either be passed in the HTTP headers as 'modAuth', or in a REQUEST var as HTTP_MODAUTH. The value will be $modx->siteId, which is set on a new install, and loaded when MODX is loaded.
Hope it helps, and yes Lucas has good point, you will be doing yourself a favoir going with ExtJs.
Regards