Knocking sound, rod bearing or torque converter etc.

Upload it to YouTube first; then you can link here.

 

If the head gasket is leaking, into the cylinders, you'll get the knock.
Is it constant or only a few seconds on start up?
Shut it off when it knocks, wait a few seconds, start the car and wait for the engine
to start, does it knock or run okay? If after 2 or 3 times of stop/start it stops knocking,
it's likely a head gasket.
Is the coolant tank low? It's on the passenger side of the car.
You should try to find someone who knows the Prius.... $6000 is WAY too much for
engine and labor.

 

Just make sure before you embark on this adventure that the rest of the car is worthy of your repairs interiors and good shape there's no leaks water's not getting into the car the armrest on the door panels aren't caving in when you put your arm there to rest the center console hinge isn't broken and ruined and ripped off and goes flying across the car every time you go to open it Little things like that because you can't buy most of that stuff for the generation 3 easily anyway for the generation two believe it or not you can still get most of those items but you will never need them and that's all I can say about that We haven't had a generation 3 that's been worthy really of these kind of repairs We had a 2013 we put an engine in drove it a few months now we're back to noises and so on and so forth but reality is the car isn't really in any kind of shape worthy of the fix other than the woman says it's mine and I want it she's in a generation 2 right now which is in twice the condition of regeneration 3 and still is talking about fixing the generation 3 and I basically told her carry on go right ahead just don't make me be involved because it's going to be a sad trail of tears all the way to your bank account and may still have no running car but be out money.

 

Try swapping coils in cylinder 2 and 3, see if P0302 becomes P0303. I suspect it won't.

EGR ever cleaned?

 

This is for a generation 3 with all of those misfire codes that's for three of the 4 cylinders and etc The likelihood of that it's pretty slim actually one or two cylinders popping off because of something happening certainly but three are all four just missing it random and the coils all match came from the factory that kind of stuff It's to me that's kind of unlikely usually with this particular engine designation this starts happening when the fires getting put out in cylinders generally from water that's in your cooling system that's now getting into your combustion system and it's not supposed to be eventually or the high likelihood eventually you'll come to this conclusion how much you spend getting there I guess is the trick.

 

Double-check that second set; I'm not aware that P050x codes are even possible in a Gen 3 Prius.

The P030x codes are nothing specific to ignition coils: they just mean that fire isn't happening consistently in those cylinders, for any of a number of reasons. It's up to the human to work out why.

 

Yeah you can do all that I generally run real spark plugs made by NGK or denso and my coils are all aftermarket made by some company that specializes in coil over plug applications and make nice looking stuff very reasonable in price I have them on a bunch of cars and have had no problems with them so generally I don't go swapping out my coils and whatnot for this particular model because usually the fire is getting quenched way up the line from the plugs this just one of those things I'm not going to throw $249 of parts at the thing when my pretty much know the engine is fubar so there's always that see Toyota's pretty consistent once you find this stuff it's pretty consistent across the whole model That's why the generation 3 can't come around here no more it is no good for me this is things you know for people that'll be out of a vehicle before 140 or so thousand they have money making payments get out of payments in the new ones very quickly and so on We do not do that We are in it for the long haul 500 plus thousand we're not looking to make changes every couple years just because but we need everybody else to do that don't get me wrong everybody can't be like me that would not be good.

 

Just make sure that if you decide to replace the engine, the rest of the car is worth the trouble. (Interior not trashed, minimal rust). If that's the case, you really made out.

 

Links on @Mendel Leisk signature will be of some benefit.
Well....maybe not the block heater.
Then someday the G3 might once again be...... Ship_shape.

Yank the plugs.
Bore-scope.
Done.
Everybody NEEDS a decent bore-scope....especially in Texas.
(MORE SO if you have case-gauges, and a ballistic chronograph....!)


The more definitive test would be to spend $30 (or borrow from a parts haus) a cylinder leak down tester.
THAT is the definitive head gasket go/no-go test.

 

Top two links in my signature have EGR cleaning tips and links. To see sig on phone turn it landscape.

 

Were P035x codes what you meant in post #5 when you wrote P050x?

 

Ah. Yes, those are real codes, specific to the confirmation-feedback signals from the igniters.

 

2010 model year is the commencement of the EGR system, first year of Gen 3. The same EGR system (more-or-less) esists through the rest of gen 3 (2010~2015 model years).

You do need to pull the full EGR system, cooler, valve and pipe. Plus the intake manifold, which has the final leg of EGR passages on the way to intake ports (which also should be cleaned).

The first couple of links in my signature have tips/strategies/links. Also tips on how to clean cooler, how to avoid undue coolant spillage.

 

If you aren't going to cleaner the cooler, there's no sense in cleaning the rest.
Or clean the intake manifold ports....

How easy or hard it is depends on your skills, and tools you have.
For me, it's easy. For others, it's difficult.
But it's one of those things that kinda needs to be done.