I may have gotten to the bottom of this...
I had this problem, and in my case one of the configuration files on the Replay had become corrupt. This prevented the unit from connecting, and also made it think that it wasn't authorized. It took a while, but I just figured out how to get my unit operational again (without losing any programming) by using extract_rtv5.
If you're not tied to keeping the programming, then a factory reset is definitely the way to go (because it's so easy). In my case, though, I had around 170 shows stored on the drive, and some of the Replay channels can't be reprogrammed because the shows are on hiatus. Thus it was worth it for me to pull the drive and experiment with extract_rtv5.
If anyone still has a system that's stuck on the service activation screen and wants to try to recover it, the following may help. Before proceeding, let me say that this should be done only as a last resort, as it may not resolve your problem, and could conceivably make things worse. Also, There may well be a much easier way to do this (that someone who knows the internals better than I can put together), but these steps worked for me:
1. Use RTVPatch to prep another drive (of any size), install it into the unit, and do a factory reset.
2. Configure the unit (via the setup screen) EXACTLY as it was configured before the problem occurred. (I'm only talking about the setup screen here... not any show information.)
3. Pull the new drive, and use extract_rtv5 to read the file sysconfig.reg. (This can be done using the command extract_rtv5 -p1 -e ./user/Registry/sysconfig.reg)
4. Write the file from the "good" drive to the "bad" drive. (This can be done using the command extract_rtv5 -p1 -w ./user/Registry/sysconfig.reg sysconfig.reg)
5. If you're lucky, then step 5 was successful and you can move directly to step 6. In my case, the good file was much bigger than the bad file, and extract_rtv5 couldn't write it. (I think that extract_rtv can only write to the drive if it doesn't need to play with the file allocation table.) If extract_rtv5 can't write the file, then you'll need to edit it to make it smaller. Fortunately, the file is in XML format, so editing it is reasonably easy. I simply removed entries that didn't appear to be related to network or authorization (such as the input settings), and was eventually able to write the file.
6. Re-install the "bad" drive (which has the updated sysconfig.reg) and turn on the Replay. If all goes well, you should no longer be trapped on the activation screen.
7. If you had to modify sysconfig.reg in step 5, then you need to go into setup and re-establish all of your settings. This will likely cause a re-connect. In my case, the unit froze when attempting to combine the data, but a reboot caused the unit to come up just fine. Your sysconfig.reg should now be much larger, so you should be able to pull the drive again and use extract_rtv5 to copy the "good" copy (which may still contain entries that are missing in the copy that's on the machine). I did this just in case. Once the good version of sysconfig.reg is on the drive, you can reinstall it into the Replay.
8. The unit should now be restored to normal operation.
Hope this helps.