This page allows you to generate OAuth signatures using a known good OAuth library, OAuthSimple.
This way you can quickly identify if a 401 authentication error received from the LinkedIn API server is due to a bad signature or another issue.
To reproduce your API call, input all of the data from your original request, including the authentication tokens.
Don't forget to set the nonce and timestamp to the values you used.
An OAuth signed URL should match regardless of the generating library. If the signatures differ, you know there is a bug in your OAuth signature code.