If your lights are all dim and you have a new alternator and battery, it sounds like bad grounds. What people don't realize is these cars are getting OLD. Mine for example is a 2000 Si so its 15 years old. Crud, corrosion, etc, builds up and all creates a lot of resistance. Get some electronic parts cleaner and spray down the connections in the plugs then use some electric grease to prevent further corrosion.
To test your alternator in the car, crank up the car and let it idle. Turn on all our accessories,
EVERYTHING, to their highest settings. Then disconnect the GROUND on the battery. If the alternator and connections are good it will continue to run. The RPM will go up due to the IACV opening to accommodate the load on the Alternator.
If the RPM starts jumping, get a vacuum gauge and put it on the manifold (T into a vacuum line). Do this test after you turn all your accessories off and follow the steps that typical come with the gauge or just google it.
http://www.hemmings.com/hsx/stories/2012/02/01/hmn_tips1.html
Here are a few fundamental vacuum readings that you might encounter while testing your engine:
- A steady reading between 15 and 22 inHg is normal for most engines. By snapping the throttle open and closed, the needle should drop to 5 inHg or lower before stabilizing at 15 and 22 again.
- A low reading that stays steady (perhaps around 5 inHg) indicates a vacuum leak at the intake manifold or carburetor. It might also be something as simple as a disconnected or leaking vacuum hose.
- A reading of between 8 and 14 inHg could be telling you that the ignition timing is incorrectly set or that piston rings are leaking. It might be advisable to break out the timing light and the compression tester at this point.
- If the needle is vibrating rapidly between the 14-19 inHg marks, it could be a sign that worn valve guides are allowing the valves to move around.
- A bad head gasket will usually result in a reading that fluctuates between 5 inHg and a lower than normal reading.
- A higher than normal reading that holds steady could mean a restricted intake. This could be a clogged air filter or a stuck choke on a carbureted engine.
- When the gauge's needle swings across a 4-5 inHg range around the normal reading, it could be a sign of incorrect carburetor adjustment (which should manifest itself in other ways, too).