Welcome to PriusChat!! The "electric engine" starts, or turns over the Internal Combustion Engine (ICE). Hope that answers your question.
Gen 2 Prius' sold outside of the United States have an all electric mode that you engage by pulling the windshield wiper control arm back... They removed this from US vehicles because some states wanted 150K mile warranty on Hybrid battery and that all electric mode if over-used will shorten hybrid pack lifespan. The system still exists in your car and myself and others have installed some wiring that someone sells to restore that function. But once you recover that feature myself and others will attest to the fact that you will almost never use it. Prius battery packs are tiny compared to a true electric car and you're gonna be lucky to get a mile down the road once you've drained that battery down and then the gasoline engine has to turn on to charge the battery up again. What's more the all electric mode will only work when the computer will allow it once the car is at optimum operating temperature, as well as fully charged and driving slower than 26mph... And while this feature could be valuable if you're driving away from a crowd of people and you don't want to blast them with air pollution the basic reality is that Prius are designed to function using both the electric motor and the gas engine and it's pretty much a totally worthless vehicle to drive in many ways if you only use one of the systems instead of both of them.
On non-NA Prii EV mode is engaged by pressing the EV button. The control you speak of is the Coastal hack. The following is just an observation – no judgment, either way, is made. The question was: to which you spent 2 ½ paragraphs: talking about the complete opposite question – "How difficult would it be just to operate my gen 2 Prius with only the electric engine?" ... but nevertheless finally bringing it home by answering the question in the last half of the final paragraph.
Most people are less thorough than I am... Being brief isn't very fun... I like to offer lots of additional information... Not only is it often valued by the person asking the question but it builds trust and sometimes even leads to friendship... People who are too brief don't get that! I've been told more then once in a private message that they'd rather just chat with me privately because the thread they started is not helping them as much as I am... So there you go, that's my rebuttal.
An electric motor/generator called M/G2 is geared to the wheels, it is always pushing the wheels, or being pushed by them, when braking. The internal combustion engine is not geared to the wheels, it interacts with another motor/generator called M/G1 to combine to add to M/G2's push. The engine can never act alone to propel the car. (In fact the Neutral gear does not effect the engine, it just powers down both motors) About 30% of the engine's torque pushes against M/G1 producing electricity, this allows the other 70% of the torque to push with M/G2, helping move the car.
oops looks like I misread that question... I thought it said "with" not "without." Apologies... I'll try to be less sloppy in the future...
