Yes, but not with the same model if the broken one is obsolete and certainly not for free! Upgrading is a whole different matter. As long as your receiver can still operate under the current system E* won't upgrade it. For instance, I had a model 1000 (8+ years old) still operational until recently. The whole "upgrade" situation is becoming a big ?? as there is mounting pressure for E* to replace all the older MPEG-2 equipment with MPEG-4 capable units sometime in the near future, but that's all just speculation - there's nothing on record from E* about that AFAIK.
Even leasees have to pay to have defective equipment replaced. During the warranty period (1 year for receivers, IIRC) it's free but after that there is some cost, at least the S&H fee ($15-25?) if not more. I'm not clear on all this. The DHPP @ $5.99/mo. reduces that substantially, but there could still be some cost, like $29 min. for an installer to come on-site if you need one (vs. the usual $99). Check the on-line information about DHPP or search these threads for more on that. There have been a lot of questions about free replacements outside the warranty period for leased units and IIRC the consensus is "nada"...