2000 Acura RL Difficulty starting sometimes

Electrical problem
2000 Acura RL 6 cyl Automatic 128000 miles

1)When I put the key in and turn, sometimes it takes three or four attempts before it "catches" and starts. Otherwise it just clicks and nothing happens. The dash lights come on normally and it goes through the diagnostics properly. I think the battery is about two years old.

2)Also, the security system appears to work intermittently.
Sometimes you can arm and disarm the alarm from the keychain, other times you can't. A new battery (in the keychain) doesn't have an effect.

Do I have an overall electrical problem or are these two distinct problems? Number 1 is clearly the more worrisome.

Thank you for any help you can provide.