2002 Ford Expedition XLT 5.4 4WD won't start! Rapidly clicking when trying to crank?

I've been having some problems with my Ford Expedition XLT 5.4 v8 triton 4wd recently.

About a week ago I drove it to see the family a few miles away and when I got back in it wouldn't crank, all I was getting was a rapid clicking noise. We brought the battery to Autozone for them to test it and it was working fine, and then we took off the altenator and brought it end which turned out to be bad, so after replacing it, it started up and I drove it back home.

I then went back a few days later after not driving it and it cranked right up perfectly and I drove it to visit them again, I got the exact same thing again, where it was making a rapid clicking noise. This time we pinpointed where it was coming from and it was coming from a little thing bolted to the firewall which autozone called it a Starter Relay/Selenoid, below is a link of what it is.

http://www.urqualitysolutions.com/New-Solenoid-12V-15-150-SAZ-4201DX-Starter-Relay-7-1035-7-1035.htm

From what I've read, if the starter is bad it'll do one click and not rapid clicking noise like this little device is making. Also that a common occurence is that possibly the cables have gone bad/aren't connecting well. I will be tryig this later today when I head on over but was wondering if anyone else has any ideas as to what it might be incase that doesn't work and i'll have to take off the starter to get it tested.

If the contacts are solid
Yea replace that, they crack, dry up where I'm at. You're hearing it there, the contacts on the inside are wore (break apart the old one)
A single click is a relay working correctly(usually)
Your car is funny with that honking thing and solenoid, the "solenoid"(plunger and contacts) are mounted/in to the starter, its otherwise usually a little box relay in fuse box to solenoid.
your is easy to reach though, and cheap(at the shop so cheap it's worth just tossing it in then trying to see if its ok, not gonna break in the next 20 miles)

OR your starter is shot, shorted to ground(battery disconnected: look for continuity between starter solenoid output, starter input, + to ground, it should be quite a massive resistance if its good) making the relay jump like a madman

But that would've been less intermittent.

Contacts in relays and solenoid s can be

Hope it helps, oh and the battery better be charged and happy but if no worky, disconnected for diagnosis jamming probes around for continuity

Big Fords are famous for corroding the INSIDE of the positive ( red wire ) battery cable clamp. Pull that cable clamp off the battery post & scrape both the inside of the clamp & the sides of the posts, using a small pocket knife blade. If that helps, most all car parts stores have a small wire brush designed just for that job. Use the wire brush on both battery cables & make a mental note to do it about once a year. ALSO, in '02, Ford tried a 'sheet metal' battery cable clamp, instead of the solid lead old fashioned clamps - They didn't work. IF you truck has the thin sheet metal cable clamps, you'll have to replace both of those with the old fashioned solid leads kind. I had the basic same symptoms on my '02 Grand Marquis. As I had experience with the corrosion problem, I tugged on the red wire/positive wire, & the sheet metal cable clamp tore in half - The corrosion had eaten into the sheet metal & weakened it beyond repair.

You are not getting enough voltage to keep the solenoid engaged. Either the battery is not putting out enough voltage or the wiring is not conducting enough amperage to provide enough voltage to the solenoid to keep it engaged. Or the solenoid is bad.

Thanks everyone! This really helped and possibly saved me hours/hundreds of dollars from taking off the starter and potentially messing something up. It turns out it was just a very small amount of corrosion on the terminals, even though I did clean them I didn't clean the clamps, but even then there was such a insignificant amount it's quite shocking that that was the cause of all my troubles. I will definitely be switching out for lead ones in the future. Again, thanks so much guys for all the help.