The most commonly referenced passage in relation to service is probably Matthew 20:28 where Christ says,
"...just as the Son of Man did not come to be served, but to serve..."
With the Lord Himself saying His role is to serve others, rather than be served by others, it would be easy to focus on "acts" or "action." Without question, I believe you can identify a believer by what and do, but the key difference is what Christ knew -- the heart.
In various points throughout scripture, we are told to "wait" (ex: Psalms 37:7) or "meditate" (Psalm 19:14). But nowhere in scripture gets my attention like Luke 10:38-42.
This is the famed "Brady Bunch" passage: Martha, Martha, [Martha]... In the 70's sitcom it was "Masha, Marsh, Marsha."
Clearly, service is important, but within the right set of priorities.
If you get so busy helping your church, that you neglect to be the Church, it might be time to step back.
If your volunteer calendar gets in the way of your personal devotion calendar, it may be time to rethink why you are volunteering.
If your desire to serve others is rooted in the approval or expectations of others, it may be time to step back and refocus on the main thing.
Service to others is important, but it does not distinguish a believer. Service is not limited to His children. What sets the service of a believer apart from that of a non-believer is the who and why. Believers serve the image of their Savior, expressly and solely (or should that be soul-ly) to glorify Him.
Please, go and serve others, but do it as part of a holistic worship of our Heavenly Father.