it would be helpfull if you could tell us how many volts your battery has, Key Off Engine Off (KOEO) and how many volts Key On Engine On (KOEO)
Chattering (clicks) at the fender solenoid usually means the battery is low or connections from battery are dirty. (you've replaced cables)
One loud click when the battery is up, I go after the bottom connection of the braided cable between the starter soleniod and the starter motor itself.
Usually just loosen and retighten does the trick. Happens about once a year.
(you've replaced starter)
Low volts on a standing battery doesn't neccessarily mean the battery is bad, could be the ALt isn't charging enough.
If Alt is putting out around 14 - 14.5 volts the battery should hold in the high 12's engine off.
Harbor FR8 had DVOM's for $4 Last week. AZ $20 on the shelf. Walmart? I dunno. $7 when i bought mine 6yrs ago. They give such a wealth of info.