Digital electronics rarely fail in a way that makes them work but work slower than normal. I suppose it’s conceivable if the analogue side of things (antenna, etc.) has been compromised in some way.
There are many factors affecting the time to first fix, but your times sound reasonable depending on terrain. My Edge 800 was perhaps a fraction quicker when used daily, but I still had to wait after packing my keys, putting on my helmet and gloves, etc.
As you’ve noticed, riding off before it has a solid fix often means the dumb thing never gets a fix.
The latest GLONASS-equipped models may be slightly quicker, though not necessarily because they have GLONASS.
None of the Garmins I’ve tried have been anywhere near as quick as my iPhone, which gets an accurate fix in urban canyons in 10 seconds flat.