Should battery be dead on a Chrysler 300 after sitting 7 days?

No, the battery on a Chrysler 300 should not be dead after sitting for only 7 days. Typically, a healthy car battery can hold its charge for several weeks without starting the engine.

A car battery can get discharged when:

Electrical Drain

- Interior lights or any switches left on

Faulty or Old Battery

- Corroded/loose battery cables causing poor connection.

- Sulfation which builds up on battery plates reducing power

Charging System

- Faulty alternator

You can try boosting it but if that does not work it is more likely a battery or alternator issue and have that inspected.