Misfiring at idle, and running lean. Lots of info inside.

[shift_down]

Car:
Ka24de-t
Blow-through MAF setup
Problem:
1)
Gauges, cluster, and radio don't turn on unless I rev the car up to 4000rpm one time, then everything lights up and I can let the car idle and everything works fine.
2)
Car constantly misfires on random cylinders; no order of misfiring. This happens once it gets warm.

Helpful Info:
1)
I got a brand new battery and the battery went completely dead after 3 days.
2)
Idle AFRs start at around 14.5 when I start the car, and slowly work their way up to 20AFR when it gets warm.
3)
I hooked my battery up to my friend's car battery, and left both cars running. When I did this, my AFRs started at 14.5 and slowly worked its way up to 16-17 when warm; never getting passed 17AFR. ALSO, the car BARELY misfired at all and idled nicely at 900rpm
4)
Compression is 210psi across all cylinders
5)
Timing is 20* BTDC (stock KA24DE timing)
6)
Enthalpy Tuned ECU

What I Tried:
Tested alternator twice - checks out good
New battery (died within 3 days)
New plugs
New wires
New dizzy cap
New rotor
New CTS

Any Ideas as to what is going on?
-Could something be draining the battery constantly?
-Could the battery just not be strong enough?
-Could the alternator just not be strong enough?
Thank you