I have a Dropbox folder that syncs locally to my computer so the library is residing on my computer. I don't understand why it wouldn't run from that folder. It shouldn't be any different than moving the iPhoto to a desktop or other folder. I understood iPhoto to be able to run from a library on an external hard drive and this should be less complicated that that option. Unless it is trying to sync different versions or something. Can you please provide more information? At this point I am just trying to move a library from one computer to another.
This is what you said:
When I try to open the library from the new computer (holding down the option key and navigating to the library on dropbox), it doesn't let me open it.
From the new computer you're accessing (or trying to access...) the Library on the Dropbox server.
An iPhoto Library isn't just a collection of files and folders, it's really an tightly interlinked ecoystem of data, metdata and dabases, and the process of moving it to a server and off again does not guarantee the integrity of the Library. Simple flaws in copying because - for instance - the file system on the Server doesn't recognise some element, or doesn't know how to use it - can render the Library useless.
To migrate a library:
To move an iPhoto Library to a new machine:
Link the two Macs together: there are several ways to do this: Wireless Network,Firewire Target Disk Mode, Ethernet, or even just copy the Library to an external HD and then on to the new machine...
But however you do choose to link the two machines...
Simply copy the iPhoto Library from the Pictures Folder on the old Machine to the Pictures Folder on the new Machine.
Then launch iPhoto. That's it.
This moves photos, events, albums, books, keywords, slideshows and everything else.