Do I rate the 1st Marine Divison combat patch for being deployed to Djibouti for ten days and in CENTCOM for several months at sea?

No. You must be a SOLDIER at the time of the deployment to rate a combat patch... Deployments with other branches DO...NOT....COUNT

There is no "combat patches" for the Marines. The unit patches are not authorized for wear on any uniform.

AR 670-1, Section 19-17:

19–17. Shoulder sleeve insignia–former wartime service
a. General. Authorization to wear a SSI indicating former wartime service (FWTS) (SSI–FWTS) applies only to Soldiers who are/were assigned to U.S. Army units that meet the following criteria in subparagraph (1), below:
(1) The following criteria are required for wear of the SSI–FWTS:
(a) The Secretary of the Army or higher must declare the theater or area of operation as a hostile environment to which the unit is assigned or Congress must pass a Declaration of War.
(b) The units must have actively participated in or supported ground combat operations against hostile forces in which they were exposed to the threat of enemy action or fire, either directly or indirectly.
(c) The military operation normally must have lasted for a period of 30 days or longer. An exception may be made when U.S. Army forces are engaged with a hostile force for a shorter period of time, when they meet all other criteria, and a recommendation from the general or flag officer in command is forwarded to the Chief of Staff, Army.
(d) The Chief of Staff, Army must approve the authorization for wearing the SSI–FWTS.
Note. Units are not authorized to modify their SSI or SSI–FWTS without prior approval from the DCS, G–1. A mirror image SSI–FWTS is considered a modification. In addition, TIOH must approve the design of any modification and authorize its manufacturing in accordance with paragraph 2–3.
(2) Personnel who served in a designated area as a civilian or a member of another Service, but were not a member of the U.S. Army during one of the specified periods are not authorized to wear the SSI–FWT

Pay particular attention to the last bullet. Even if you were in Djibouti supporting an Operation that warrants an SSi-FWTS, but were with the Marines at the time, then you do NOT rate being allowed to wear it.