It'd help to give your battery an overnight charge to make sure it's fully charged, then start diagnosing from a known point. Regarding the hazard switch light - if it doesn't go out after about 15 minutes the "fix" is to disconnect a battery lead for a few minutes, then reconnect. That should reset any "stuck" modules.
I'm not convinced that driving the car will ever fully charge a depleted battery - I periodically give mine the overnight charge treatment if I haven't used it much.