Your PayPal Express Checkout and/or Website Payments Pro module settings require 4 components to be set correctly in order to talk to PayPal successfully. If any one of them is incorrect, you'll not be able to authenticate and submit transactions:
- API Username
- API Password
- API Signature
- Paypal server: live vs sandbox
Normally you would obtain your API details from your real PayPal account profile, and select the "live" server mode. THIS IS THE BEST ROUTE.
You can only use "sandbox" option if you get API details from the sandbox site's account profile. Sandbox should not be necessary in most cases.