There are three different credentials to keep tab of during the checkout process.
First: Your sandbox.ebay.com userid and password
Second: You PayPal Developer account user email and password
Third: Your PayPal Sandbox account user email and password
The first set of credentials, are the credentials used to log into the eBay Sandbox, that allows you to do thing like list an item, purchase an item, etc.
The second set of credentials belong to your PayPal Developer account, which allows access to your PayPal developer account. This allows you to add or remove as many test PayPal Sandbox Accounts as you would like.
The third set of credentials, belong to your PayPal Sandbox account. These credentials allow you to actually test the payment of items and process them through the Sandbox Checkout mechanisms.
In order to successfully checkout an item on the eBay Sandbox, please do the following on the same browser.
1. Log into www.developer.paypal.com using your PayPal developer account credentials
2. Now, open up a second tab, and enter www.sandbox.ebay.com into the address box
3. Log in with your eBay Sandbox Credentials
4. Find an item to purchase, and begin the transaction process
5. Agree to the payment process through PayPal, once you are asked for your PayPal credentials, enter in your Sandbox PayPal credentials
6. Complete Checkout