Many trouble codes

[timf1981]

My neighbors 2008 prius
He has had it 2 years
In the past he has replaced both front rotors, one headlight bulb, and the 12 volt Battery.
This week big red triangle light on dash came on. There is also a (circular brake light on?)
And the tcs light is on. Not sure if they all came on at once. Car seems to run ok. I asked him about how much the car runs on Battery. He believes it never ran much at all on just Battery. I took it fir a short ride. It seems to run fine. The engine will turn off at a complete stop. But kicks right back on with light acceleration.  Big battery is I believe at 58%. All 14 cells appear to be at 326.35 volts.
He hates cars and if it runs he dosent pay much attention to dash lights. 
He took it to dealership. They think it needs a new inverter converter. They did not spend much time digging into it. But they gave him an estimate for $5700 for new inverter.
Here are all the codes I read. I currently do not know if the ac worked this summer.
If you are familiar with these codes.  Which ones are related?
I will check the inverter pump first. I believe this car has a inverter coolant pump recall. I don’t know if it has been performed.
Are all the ac codes related to the main inverter converter?
Does the ac have it’s on inverter?

OEM  present codes and OEM read codes 
B1421 solar sensor circuit passenger side
 B1473 air conditioner inverter  start up signal system malfunction
 B 1498 communication malfunction (air conditioning inverter local) also OEM pass code
 
OEM current codes OEM history codes
 P0A08 DC/DC converter status circuit 
P3108 lost communication with air conditioning system control module.
 
OEM history codes OEM read codes 
C1310 malfunction in HV system
 

[Saxmaniac]

Have a look at Prius Chat forum in America as there's loads of very technical people over there. Not so many here by the looks of it but would never trust anything a dealer tells you, they will just guess at the most expensive thing. They've probably never checked anything other than the fault codes 

[flash22]

The codes are a symptom of the problem not the cause, yes the HV/Motor communicates with the A/C system, a common issue seems to be the A/C amplifier goes bad if that's sending bad/no information the inverter will get confused and go into a limp home mode what may disable the inverter - if the A/C is requested it will start the petrol engine

Edit. Pull the A/C fuse and see if that does anything

As for the pack you need to view the cell voltages to really see if the cells are performing

Where are you in the states ? Anywhere near New York/Staten island ?