Formulating a product goal for our CRM

Our team (we're only three developers at the company) have a difficultly with formulating a product goal which makes it very difficult working with Scrum.

I'll bet. Where's the Product Owner?

We work with our companys CRM, a non commercial product, and we have different departments using different parts of the CRM which is quite unrelated to each other

What forces lead to the CRM becoming a single product?

Our team (we're only three developers at the company) ...

You have one third of a Scrum Team.  That would be the reason you are having such difficulty with the Scrum framework.  From your description you do not actually have a product identified or anyone responsible for the success of that product.  No one to help the team become more efficient and effective in their efforts to deliver value to stakeholders. 

If you are trying to use Scrum as a basis for managing a list of to-dos it is going to be more problem then help.  

Honestly your question raises more questions for me than it does any kind of possible suggestions. 

Sorry, I was a bit unclear. We're three developers plus a product owner. 

A Customer Relations Management (CRM) is a system by definition. It could also be seen as a product made up of different features.  Formulating a Product Goal for an internally created system for internal use only is no different than creating one for an external product.  For example, Salesforce has a CRM and there is a good possibility that they have a product goal for that CRM.  In fact, they may have goals for different segments of the overall product. 

This is where your Product Owner comes in.  What is the reason that the CRM exists? What problems does it solve? What value does it deliver? Derive a goal from those questions.  For example, the Product Goal could be "to deliver the relevant customer information to the internal employees at the time that they need the information."  I will admit that is not a great one but it is still a product goal. Another example would be to "Do everything that Salesforce does".  Again not one I'd actually suggest but it is still a Product Goal.  The Product Goal then helps to determine what type of changes are needed to be made to the product.   

...we are trying to work more and more in alignment with Scrum.

What is driving the desire or need to align more with Scrum? Could it be that Scrum is not a good fit for you since you have such a small team?  Is the environment complex enough to need the benefits of Scrum? 

Thank you Daniel, that's a helpful answer and I have been entertaining the same thoughts. Perhaps we need more than one product goal. I guess I didn't think it was a good idea because in that case we either need to distribute our sprints to so that we work with one product goal in one sprint and another in the next sprint, or we need to work with more that one product goal in a sprint and hence need to have more than one sprint goal. The second option is kind of the way we work right now, that is, we add into the sprint whatever backlog-items that feels most relevant to solve at the moment and they usually don't have anything to do with each other but we don't formulate any sprint goal. I think it works quite well for us to work that way and to me it feels very natural. We started talking about Scrum in since we want to work more efficiently, but it could very well be the case that Scrum isn't a good solution to us.