First, if you just replaced the battery and positive lead, check all of that to make sure you have a good connection. I've had trouble starting the car because one of the leads wasn't clamping down tight enough. Also make sure you check all of your main grounds.
Second, check to see if the main relay is bad (this is probably your problem). Turn your key two clicks forward. You should hear your fuel pump kick on for a few seconds and then kick off. If this doesn't happen, it's your main relay. Main relays will also have trouble not working when the temperature in the car is high if they are going bad.
If your main relay is fine, check your distributor cap and rotor for corrosion. These are cheap to replace.
Then check your fuel filter. It may need to be replaced.
If you hear clicking from the starter it could be a bad starter solenoid like stated above. If you replace the starter, I would recommend an OEM one. They are more expensive but last quite a bit longer.
Last, it could be an ECU going bad. Swap out yours with a known to work ECU and see if it helps.