Here's what I would do, Clean the battery first, charge it for an hour.
With the help of a friend, put a meter across the low current side of the start solenoid, and turn the key to start, see if you are getting current/voltage to the low current side of solenoid.
If no reading on the low current side, check the wiring back to the key switch, and did you check all the fuses? Keep looking until you get current on the low current side of the solenoid.
If you are getting current on the low current side, try checking the high current side with a meter. If you get no current/voltage on the high current terminals, its almost sure to be the solenoid. If you get a reading, it could still be a bad solenoid, and the contacts are charred enough to raise resistance to not to allow high enough current to get to the starter. Solenoids are relatively cheap, change it if your in doubt.
You could try the remote starting directly to the starter, but if you don't have a remote starter, be careful, its hard not to arc and mar a bolt/nut, and you are working with VERY high current.
Be careful, when working on the battery/high current side of the wireing. remember you are dealing with current that can weld steel, the usual disclaimer I take no responsibility.