Is it normal that the solo does not show the charge with these batteries?
I am charging it right now. Charge is blinking green and the blue idle light is on. Nothing else.
No, it is not. Not normal at all (which is why you don't find a lot of discussion on it). IMO it points right back to a battery pack problem. Specifically I think that for whatever reason one (or even both?) of the cells has gone dead flat and therefore the protection PCB in the pack has 'fired' to protect it (something like a fuse or circuit breaker does). This presents us with several problems, the first of which is 'unlocking' the protection circuit?
The only way we have of doing this after the pack is sealed is by 'trickle charging'. As loose cells we could have charged the cells individually, no longer an option. Chargers use a very small 'trickle current' to sense a battery in need of charging and also to 'unlock' in the case of extreme discharge (one the normal Solo circuits didn't stop before the battery crashed). Depending on how bad the fault it can be an hour or so to several days. Don't give up too soon. After that it should be more or less normal but the base issues will remain and the cells will be 'out of balance' meaning the stronger will hammer the weaker a bit on every cycle (discharge and recharge).
Balance is critical to making a long lasting, quality pack. Lots of ways to make them wrong, not so easy to get them right.
The original problem (the one that killed it) still remains of course, you did nothing to fix that whatever it was. A lame/defective cell could have 'self discharged' below safe limits, it'll do so again when the mood suits. The protection PCB could be defective and using too much current in it's full time monitoring (even after shut down). I've seen this too in the journey of building Solo packs. It could have been sloppy (or ignorant) construction of a pack with poorly matched cells (important detail, easily overlooked by amateurs). Since they are in series there's no way to correct this (charging the weak cell also charges the strong making it still stronger), it's 'cooked into' the pack
None of this bodes well for the sort of gear a guy wants to give his mother to depend on. It could (and no doubt eventually will) 'go south again' without warning and at a key time (funny how that bit always seems to happen.....). OK for personal use (if you stay aware) but you should, I think, consider the old pack? How is it doing?
For your amusement here's a factory pack with it's clothes off:
The white thing at one end is the thermal safety Arizer describes, something I put in the packs I built but never found in an 'aftermarket' one like you have. IMO Arizer put this in for a reason, not to waste money and introduce another potential point of failure. It's a safety feature not found on cheap copies. Which can also have substandard or poorly matched cells or cheap/defective protection boards.
My advice it 'jump start it' if you can, but save it for personal use where you can keep an eye on it over time? Mom will do better on a battery, even a worn one, without such surprises.
OF