Possible inverter fail? 2002 Prius

I need to know what the symptoms of an inverter fail.
My Son was driving from St. Louis to Kansas City in a torrential downpour when the car suddenly lost power. The engine was still on but would only go 2 miles an hour. I towed back to St. Louis to stealership. Multiple codes later they said it would cost $3800 for a new HV battery, Ecu and to clean out an overfill of oil via my son.

I decided to do it myself. When picking up vehicle from dealer there was no power at all left in car. Would not even turn on. I bought a rebuilt battery from priusrebuilder.com and installed. By the way a very easy thing to do, swapping out the battery. Although quite heavy.

However when starting I still got the warning triangle with ! and also check engine light and on the main graphics display a PS, a pic of a battery in grey color and a pic of a car with ! in it colored red.

And the vehicle started but still has no power and only goes 2 miles an hour and not even enough power to go up my sloped driveway.

I checked the inverter coolant resevoir and there is no turbulence. The battery may have been due to be replaced but I think the mail problem was the inverter going out. What can I check to validate this. All the codes the deal gave us was on a voice mail he left and unfortunately it was deleted.

Need some help to decide what to do next. I already spent about $1100 to no avail.

 

I replaced the HV battery with one from priusrebuilders.com. Turned car on and engine started with display showing energy consumption going from engine to battery to fully charge it. Then shifted into N still ok. Then shifted into R and ok until I took foot off brake and car started to move and immediately all the warning lights lite up. I checked codes with an Autel MS509 scanner and got codes P3100 and P3125.

 

I was incorrect about the coolant reservoir. There is turbulence in the fluid with car on so pump seems to be operating properly.

 

thanks to 3prongpaul I was able to get the codes P3100/175 and P3125/287. These are leading me to replacing the inverter/converter and pump.

 

Here is an update to this escalating headache I have been dealing with.
I installed a good used inverter in the Prius and still had the same problems. Still was getting P3100 and P3125 codes flash every time I put the car into reverse and as soon as the car moved backward.
After discussing this with a couple people the only thing left was the transmission.
It took awhile but I found one close to the house at a salvage yard for $500.
I installed (after a lot of work) and the previous problem was no longer there.
It started up fine and began to drive but then after a few minutes a code was thrown again.

This time I was getting P3006 and P3021. Battery codes. I can drive around the block a few times but doesn't have any power to climb hills or really pick up fast. This was about 6 months after first installing the rebuilt Gen1 battery with Gen1 cells that only had a 90 day warranty. However this battery didn't sit for that long. During this process periodically I would start the car just to get some charge to the battery while trying to figure out what was wrong. However it did sit for about 4 weeks while removing the transmission.

At this point I am trying to rectify the situation with Prius re-builders in Fairlawn, NJ. I was never sure if the battery was good when I first received it because the transmission problem would let me test drive the battery power.

Hopefully everything comes out OK.