I haven't used the ASI networking stuff before, but have seen lots of references to it on the net.
It sounds to me like the ASINetworkQueue class expects it's delegate to conform to a specific protocol. If it's set up correctly, you should get a warning when you try to assign yourself as the delegate of the ASINetworkQueue object but have not declared that your class conforms to the appropriate protocol. If you DO include a protocol declaration, then you should get a warning that you have not implemented required methods from that protocol.
Try cleaning your project and rebuilding, and then look carefully for warnings, specifically on your line:
[[self downloadQueue] setDelegate:self];
EDIT: I just downloaded one of the ASIHTTPRequest projects, and to my dismay, the delegate property of the ASINetworkQueue class does not have to conform to a specific protocol. This is bad programming style. If you set up a delegate, you should make the delegate pointer conform to a specific protocol.
Also, be aware that the ASI networking classes have not been maintained for several years now and are getting badly out of date. There are better alternatives out there, and you should look at moving to a different networking framework.