In teaching, we are taught that there are 6 C's to motivation (http://epltt.coe.uga.edu/index.php?title=Six_C's_of_motivation)6 C's to motivation. These are: choice, challenge, control, collaboration, constructing meaning, and consequences. I would suggest that to motivate players in ways other than those already mentioned (recaps, social times, frequent breaks, etc) I would try to focus on helping the DM/GM provide more of the 6 C's.
With regards to choice, try to think of what gaming choices you can promote/support that would favour the interests of the unmotivated players. For example, if they are bored by combat, start championing group approaches that favour diplomacy, evasion, or intrigue.
When thinking challenge, try to pick fights/missions that suit but stretch the abilities of the members of your group. Fight each other if you have no appropriate alternative, but pick and choose your battles so that everyone can contribute with a real sense of (manageable) threat present.
Giving players control over how and when they will participate promotes player buy-in, increasing motivation. Try not to let any one voice or "group think" dominate your play. Be the "devil's advocate" when you can.
Collaboration is implied in any gaming group, but you can take it on as a personal responsibility to augment the effect of another player's desired course of action by aiding them in ways that give bonuses or further alternatives for action - even if it's not something you might normally choose to do.
Constructing meaning is harder for a player to accomplish than a DM/GM, but basically, in order to motivate someone to do something, it needs to personally have meaning for that player. Perhaps, in character, you can start wagering gold on the outcome of various encounters, or suggest why what the group is doing next should matter to the unmotivated player (in character).
Finally, consequence is a matter of recognizing achievement when it happens. Showcasing an unmotivated player's achievements motivates that player to continue along that line in the future. Be descriptive where possible.