I know it's a basic question, but are the services set to automatically start?
When you start them manually, do they keep running or do they stop shortly after? Could be an issue related to the login account specified (if you are using a named Active Directory account).
Just as an aside, you don't have to have the SSIS service running to execute packages - this service just handles the developer experience when connecting through SSMS (and a few other small things mostly unrelated to package execution). The SQL Browser service may not be required either, depending on your environment.
Tim Mitchell, Microsoft Data Platform MVP
Data Warehouse and ETL ConsultantTimMitchell.net
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