Hi Dave - the click from the starter sounds like it could be just the solenoid kicking in. This operates the yoke that engages the pinion onto the starter ring gear, but also makes the heavy current connection to the starter motor itself by shorting together the two studs at the end of the solenoid body. If the battery is fully charged, check the engine earth strap and make sure that none of the clamp connections are corroded. Hopefully that should kick the starter into life!
As for the brakes, if there is a large air lock in the system (from replacing parts or fluid for instance) it can sometimes take some time to get the fluid back into the master cylinder. I remember I had to pump my clutch pedal a lot to prime the cylinder before I was able to bleed the slave cylinder. perhaps the same thing has happened with your brake circuit?
Good luck, sounds like you are on the home straight at any rate
Lauren