I do think the problem is electrical, a bad ECU normally will not keep the start button from working and making the starter spin. You need a wiring diagram and a multimeter in order to check the electrical system. It becomes a process of elimination starting at the battery, fuses, solenoid, ignition switch, starter switch, then ringing out the wiring throughout the ignition system. I chase these problems for a living and it's very hard to pin them down on a blog post or over the telephone. If you are not familiar with reading wiring diagrams and using a multimeter you are basically left with shotgunning it by replacing parts until you fix it and that can be costly. My first thoughts would be to check the fuses and be sure you have voltage to the solenoid, then eliminate the possibility of a bad ignition switch, then the starter switch. If all that checks good and you have a good battery the solenoid should at least click when you press the start switch. If it doesn't click then make sure it is properly grounded.
Hope this helps or at least gets you started, good luck.