To answer your main question, I think that money can be a demotivator, but never a motivator. Here's what I mean: Let's assume your resources are underpaid, this will make them demotivated, but, if your resources are fairly (or well) paid, then money is not a concern for them anymore, and consequently, not a motivator. They don't even think about money anymore.
I don't think it's the job of the project manager to ask for raises, it's the job of their manager (the functional manager) to do that. Do not step into other people's territory.
Now let me give you my opinion on why your team members are demotivated. I think it's one of two options:
- The tasks you are giving them are not challenging at all.
- The project they are currently working on seems like a never ending a project (maybe you are constantly hit with change requests?). A never ending project can cause a lot of frustration.
The first problem can be solved by listening to them, getting their feedback, see what would they do with these tasks to make them more challenging. Beware falling into the "gold plating" trap though.
As for the second problem, you may start thinking about creating a phase II of the project to handle all those change requests. You need to assure your team members that the project can and will get finished.