You mention "old school receivers, no HD", so what you should have are two separate receivers each with its own coax cable going to the dish. Either of the receivers by itself should be able to power the dish, but it sounds like one of them isn't doing to properly. There are a number of things that can cause this type of symptom, so you can start checking things as follows.
The first thing I would try is to swap the two receivers and see if the problem stays in the original room, or moves with the problem receiver. If the problem stays in the room, it has something to do with the wiring or possibly the LNB on the dish. If the problem stays with the receiver, you have a defective receiver and it needs to be replaced.
If the problem stays in the original room, check all of the connections between the receiver and the dish (as far as you can anyway). There is most likely a ground block outside your house where the coax from the dish goes, then on the other side the coax that goes into the house. Make sure all connections on that are clean, dry, not corroded, and secure.
If that doesn't fix your problem, and you have easy access to the dish, you can try swapping the two coax at the dish. But to do that you have to remove the LNB assembly carefully, so don't consider this unless you are comfortable doing so.
Or, just call DirecTV and arrange for a service call.
I really appreciate the time spent trying to help me with the issue. Here is what I did.The house has been around a while and there are several cables that are not used and it has been through a few installations and upgrades. I traced the cable from each receiver to the LNB. The front receiver ran out to a grounding block on the side of the house, through one port, and up to one side of the LNB. The back receiver ran out bypassing the grounding block and straight up to the LNB. An abandoned, dangling cable by the dish ran down to the other port of the grounding block. I reconnected that cable to the LNB and connected the cable from the back receiver to that port of the grounding block...restoring a previous installation. Both worked but the original issue persisted. I removed the grounding block from the path, connecting each cable set straight to each other with a male/male connector and the problem was resolved. A quick trip to Lowe's for a new two-port grounding block and we are back in business and properly grounded. I can only assume that something was wrong with the grounding block. It also looks to me like a previous service call had determined the cable (LNB to Ground) was bad since it was just dangling by the dish. At any rate the problem is solved and I am indeed grateful for the help, and also grateful for finding this forum in case we have issues in the future.