I'm just going to suggest a bunch of random things that people unfamiliar with modding may not be aware of...
First, each version of sins has a separate mod folder, so the mod needs to be in the folder for the most current version (you can delete folders for older versions)...
Second, you have to enable the mod via the game...from the main menu, go to options, then mods (at the bottom)...if the mod is in the right folder, you should be able to select it and click "enable"...game will freeze for a bit but if there are no problems it will eventually return to normal....
Third, if the "checksum" does not change from zero when you select a mod, then either there's nothing in the folder or the folder hierarchy is not right....
Let's say you are trying to play the Distant Stars mod....then in the folder "Mods-Diplomacy v1.34" (trinity may be named slightly different, idk) should be a folder called "Distant Stars"...and in that folder should be a variety of folders (such as "GameInfo", "Mesh", "String", "Sound", etc.) and possibly some manifest files...and in those folders should be the actual entity files, mesh files, textures, etc...
If you just downloaded the mod, extracted it, and copied it into the mod folder, you probably have an extra level in the folder hierarchy, where there is a folder "Distant Stars" within a folder "Distant Stars"...
These are easy things to overlook if you've never used mods before...I'm guessing you just downloaded a mod and extracted it (as opposed to making your own), so unless you downloaded an old version or a mod that doesn't work on diplomacy, I doubt the mod itself is the problem...