two different problems here probably. the shaking problem is probably your starter or if it is after you have already started the engine it could be running rich meaning one of your cylinders is not firing. With the power loss situation it is probably the alternator. get it checked. Any problems with the battery recently?

And the mystery vehicle is?

Or are you one of those people who think every car is exactly the same?

spark plugs may be bad, causing too much fuel and not enough spark in the engine, which could flood it and make it run poorly. distributor could be shot. timing could be off. hundreds of possibilities.

Ignorant car owner who does not do proper periodic maintenance.