Dead, only the dreaded clicking noise

My GF has a 98 Amigo 4 cylinder no 4wd...its completely dead to say the least. I've tried jumping it with my optima yellow top connected to a 180 amp alternator. No luck, just clicks.

I can read the battery voltage through the OBDII connector and it reads 13.3 volts when i'm trying to jump it. I left the two vehicles connected for probably 20-30 mins. Still no luck.

This happens when she lets it sit for a week or more, but we've always been able to jump it back to life no problem. Today I realized the previous owner left the wiring/switch/relay for additional lights he must have removed. If this was left on, could that be whats killing the battery? even though there are no lights attached?

The battery is almost brand new (Auto Craft Silver, rated at 585 CCA) plus its 40*F here so i dont think its the cold

If the lights are gone, then there is nothing there to drain the battery, even with the switch on UNLESS the positive wire is in contact with the chassis or other ground point. Pull your terminal connectors off and give them good cleaning. Probably has good bit of corrosion on post between connection. Corrosion kills amperage.

My GF has a 98 Amigo 4 cylinder no 4wd...its completely dead to say the least. I've tried jumping it with my optima yellow top connected to a 180 amp alternator. No luck, just clicks.

I can read the battery voltage through the OBDII connector and it reads 13.3 volts when i'm trying to jump it. I left the two vehicles connected for probably 20-30 mins. Still no luck.

This happens when she lets it sit for a week or more, but we've always been able to jump it back to life no problem. Today I realized the previous owner left the wiring/switch/relay for additional lights he must have removed. If this was left on, could that be whats killing the battery? even though there are no lights attached?

The battery is almost brand new (Auto Craft Silver, rated at 585 CCA) plus its 40*F here so i dont think its the cold

What is the v's on the battery before you try to start it? I am no genious on these isuzus but generally speaking, if the voltage is good you probably have either a bad connection like sassee says, a bad starter relay (about the size of an ice-cube and probably in the engine compartment relay compartment) or something is up with the solenoid...
Pls tell us what voltage you have (you can get a digital volt meter for like $5 at radio shack) on your battery before you even put the key in the ignition. This may help us to help you.