Thank you guys for the quick replies...
Don't worry - I haven't connected anything randomly quite yet

And yes, it is in neutral...
So - the model number is: E10TEX4SID - Electric Start 9.9 Evinrude, 2001
The electric starter part (the one in my pic) is connected to the motor via a cable.
I have tried starting the motor by turning the key, (after connecting the +/- from the motor to the +/- on the starting battery), but got nothing. No sound, no start, no clicking noise. The battery is brand new, and I even tried another battery.
The motor does start easily by pulling on the rope starter. I've checked the fuses, they were fine, I even replaced them just in case...
Went to Waste Marine today and bought me a nice $37 Johnson/Evinrude Outboard Repair Manual... Looking through it is like looking at Japanese characters to me.... Thanks for the help guys!