When you see multiple electrical failures at the same time, and you know the system has power, always start by checking your grounds.
Since you just replaced the battery, I'd make sure the terminals (and harness connectors) are clean and tight. If you see any signs of corrosion on the harness cable or the terminals, clean it with a wire brush. (There are a thousand ways to clean corrosion from these things - Google will help you out with shaky-yet-informative videos.)
On this engine, you probably have 3 or 4 grounds. I don't have the service manual, but I'd bet they are:
- Near the battery, which typically branches off from the negative cable connects to the frame.
- Definitely one for the starter. However, unless you've been fussing with the starter, I'd be surprised if that one has an issue.
- Could be one on the cylinder head near the thermostat. All of my cars have at least one, and typically two, grounds connected to the head(s).
Also, check for continuity (with your multimeter) between the negative battery terminal and the frame and engine block. If that's bad, few if any electrical devices on the car will work.
Probably goes without saying, but when checking continuity against the frame, find an unpainted section. Most paint doesn't conduct that well.
