Already have H1 COS Approved can I return with H4 and go for COS

I left US when H4 - H1 cos was effective. Can I return to US in H4 and do COS again?

1. Petition Approved: Sep 30, 2013 with new I94
2. H1 Effective from Date: Feb, 2013
3. Traveled to India Oct 10 2013 to Dec 2013, So I left US as H1 worker, but didn't join/start work bcos of short period between approval date and my travel date, It was just 10 days and Govt was shut down to get SSN to be paid
4. Plan to teturn in Jan 2014 with H4 stamping and apply COS when project is ready to start working

Can any one please clarify if I can return in H4 and do COS? Is old H1 petition still be valid even after I get recent H4 stamping? My employer also suggesting same due to lack of project now.

Am sooo confused.. pls help..