The hybrid computer controls switching between the ICE and electric motor. When the computer issues a start command to the ICE, the engine has a little less than a second to start running; otherwise, a "failed to start" error is sent. If the computer senses that the ICE did not start, it spits out fail codes and will not attempt to start the ICE again until the problem is fixed, and the fail codes are cleared.
If the engine oil pan is overfilled (full = 3.7 quarts) it will sometimes suck oil into the intake manifold, causing the ICE to stumble when started, which results in a "failed to start" error. While this can occur in any temperature, the probability of this happening increases in extreme cold (sub-freezing) weather.
Sometimes, you can just clear the error codes, and the ICE will start successfully the next time you power up. However, if enough oil has entered the intake manifold, it may have to be disassembled and thoroughly cleaned before the ICE will start reliably within the time allowed.
Besides excess oil in the intake, the butterfly valve can also get contaminated with carbon build-up, which will also require the intake manifold to be removed and thoroughly cleaned.
Repair shops, quick-change oil centers and even Toyota dealer service departments often use automatic filling equipment to pump in new engine oil while doing an oil change, and it's easy to just set the indicator to "4", instead of "3.5", which will result in the crankcase being overfilled. Then, it's just a matter of luck whether you will have problems down the road. (To avoid this, take in your own oil for them to add; specifically, 3.5 quarts only! Or, do the oil changes yourself.)
If you have error codes indicating "failed to start", the default troubleshooting method is to check the engine oil level to make sure the crankcase is not overfilled. If it is overfilled, drain a little oil out until the level is at or below the full mark on the dipstick. Disconnect the battery for about 20-30 seconds; then reconnect, to clear fail codes. Then, attempt to restart your car. If you're lucky, this will fix the problem. If this doesn't work after a couple of fail-code resets, you will probably have to remove and thoroughly clean the innards of the intake manifold; or, limp/tow your Prius to the dealer's service department for repairs.