There are so many unknowns in a question like this. If the video is 1080p 60Hz (i.e. what fit in the original HDMI 1.2 bandwidth equivalent of 165 MHz pixel rate) then you can probably go 15m or farther with high quality cable. If the video is 4K resolution and/or more than 8 bit RGB (or 12 bit YUV), i.e. 225 MHz to 340 MHz equivalent rate, then 5m might be it. The newer HDMI 2.x 600 MHz equivalent might not even make it that far.
HDBaseT is a pretty reliable way to get < 300 MHz HDMI up to 70m. Not sure why the word LAN was added as HDBaseT is point to point connection that uses CAT 5/6 cable in a proprietary format, it is not a HDMI over Ethernet system.
HDMI and particularly the HDCP Digital Restrictions Management (DRM) system that consumer gear has inflicted on it is very, very fragile. If the video resolution changes or blips the whole link (BY DESIGN!) comes crashing down and can take a few seconds to re-establish itself. I've seen plenty of devices that operate normally most of the time but get confused if the source blips at just the wrong time and/or a few times in a row quickly. The only cure is either a cable unplug/replug or in some cases power cycling one or both devices.
The fact that putting the old cable back "fixed" it could just be coincidental, the whole sequence could easily have happened without changing cables and/or just using the direct HDMI connection.
Gear from more than half-dozen years ago tends to have more problems than newer gear as the newer HDMI chips can be somewhat more reliable. But I've yet to see any HDMI chip (among the 4 vendors I'm familiar with) that works perfectly 24/7/365 with all equipment combinations.
But to answer the original question: HDBaseT (both ends from the same vendor) for 10m to 70m range and fiber beyond that. If needing more than a few point to point then HDMI to IP is probably the best bet - but you need dedicated switches, etc., you don't put that over your regular network. Or you go with broadcast (SDI) gear as that stuff is designed to work (but it's also big $).