Take the blue wire off and, with the ignition turned on, touch it to the earth of the engine. Get someone to check if the ignition light comes on then. If it does (which I suspect it will), then the fault is internal in the alternator.

Also, put a jump lead from the negative battery terminal to the engine block itself then run the engine. If the earth is missing from the engine to the car body, you will get this sort of issue as well as the circuit cannot be made without going through another part of the engine, normally the throttle cable or similar, creating a higher resistance which needs to be overcome.

Where have you connected the red wires to? They should go back to the battery via the starter motor.

The alternator you have there is a 45/55A one. These use a "block" connection, the 70A ones use separate bolt connections.

The "W" output will be almost opposite the "block" connection area (bottom of your picture), nowhere near where you are working.

Is the alternator turning the right way? If the alternator is running "backwards" (i.e. opposite direction to what it is designed to do), then it will not charge correctly and will try to drain back through the diodes in the alternator, hence the power loss.