They definitely will not send a 501 (unless its by mistake). You are entitled to a 508 or a 510. If they try to force a 510 on you remember they are charged a $5/mo. fee but receive 100 hours of DVR recording space instead of 60 hours. The receiver will probably also be refurbished.
I had an issue like that with a 301, but it would only stay on for about a couple three seconds then turn off without being able to be powered on again. You had to unplug it and plug it back in again to get it to turn back on just to have the same results.