@Michael Bronson,
You can use the below API
curl -u {ambari-username}:{ambari-password} -H "X-Requested-By: ambari" -X PUT -d '{"RequestInfo":{"context":"_PARSE_.START.ALL_SERVICES","operation_level":{"level":"CLUSTER","cluster_name":"hdp"}},"Body":{"ServiceInfo":{"state":"STARTED"}}}' http://{ambari-host}:{ambari-port}/api/v1/clusters/{cluster-name}/services
Replace ambari-username, ambari-password, ambari-host, ambari-port, cluster-name with respective values
Note: Cluster Name should be replaced in 2 places. One in the url {cluster-name} and the other one in the json which I put as hdp
Thanks,
Aditya