I assume you are powering the dock? Many docks require external power before they will pass video.

Does the screen on the deck shut off or stay active?

If the screen stays active that means that it isn’t detecting an HDMI signal through the dock at all.

If the screen shuts off but you get no video through the receiver, you should try hitting the power button one to shut it off wait a few seconds then turn it back on (while plugged in). Even the official dock has issues getting the deck to switch to the external output but putting the deck to sleep and back on gets it sorted out.

If that still doesn’t do it plug in directly to your TV to narrow down the problem (removes the receiver as a variable). Next try a different HDMI cable, and as a last resort try a different dock. If you know someone else with their own deck you can try theirs to eliminate a hardware failure on your deck.

Slows down then freezes sure sounds like an out of memory situation, so to add to yours here they might actually want less swap. Sometimes you would rather hit the oom killer sooner instead of waiting on swap to fill.

Ideally login via SSH from another machine to figure out what is using the memory (hopefully the system is responsive enough for SSH), and if it is your critical programs causing the problem then you should consider a memory upgrade.