How do I improve an old and small tech company culture?

Wow, I feel your current struggle and need for change.
So here you don't have much control over management right?
Just my thoughts here:
A simple step as a coworker is to host a party. Begin a tradition where every end of the month you or someone else hosts a get together or go hang out at a local bar near work (so that less people have an excuse due to distance)

the goal is to build solidarity, at InfusionSoft, one of the ways this company builds a strong cohesiveness is by a monthly "tailgate" where the company sponsors a party in the middle of their headquarters building.
here is a link to my blog talking a little more about what C.Culture is not..and a pic of their space: http://unthinkeverything.blogspot.com/2014/01/what-is-not-company-culture.html
{this will only help in rebuilding friendship and some trust, as well as serve as ice breakers for any new people, which in turns in making speaking to each other about project issue that much easier}

Moving on,
Agile is a very powerful project development process and if this is not working then the root of the problem is serious lack of engagement. Being paid little definitely hurts morale, but what hurts more is a lack of pride in what one is working on. See if you can help with improving morale by encouraging others to see the value and amazing impact their product will have in the marketplace. Developing a culture is hard, and there is no real recipe because you are dealing with individual reasoning, goals and history. But you culture can definitely be guided so that the right culture is shaped for that environment, it might turn out that the culture that thrives is something you would have never expected.
Steps to any progress begin with unconscious ignorance then conscious then conscious learning and effort. Once the culture is active and it will become self sustainable and thus an unconscious process. Check out my blog post, it will guide you at least in what is not a culture, so you have a start with that.

There are a lot of similarities in your situation to my last company, where I started at the bottom in project management and ended up CEO after a few management turnovers and the Board put me in charge. My thoughts are based on seeing cultural transition from all angles.

1. It is very, very hard to effect meaningful, long term change in the company from the bottom. What is the ownership structure of the company? Who are the managers and what is their sense of urgency in effecting change? I fear it's not much, given the situation you describe.

2. You really can't hold people accountable directly but you can try to inspire from the bottom to achieve new goals. I would not focus on "analytics" but just come up with _one_ simple, measurable goal that the team can agree on and work toward together. It's like getting a really overweight person to lose weight - start simple, with walks around the block. Once a new habit is established, move on to the next one.

3. Have you identified others in the org that share your desire to improve things, and enlisted them 1-1? Cultural/organizational change takes a lot of emotional energy. You need allies or you will go crazy.

Would be happy to get on a call and get more details and work through tactics if you are interested.

Best,
Karl

culture change is the most difficult of all changes. And u may need to decide on which culture dimension u want/can push a change first. Needs a study of status-quo. i've done few of these.. maybe can help u there. But to the point.

There will be resistance.
http://dhemery.com/articles/resistance_as_a_resource/

and there will be battle.
http://www.scrumalliance.org/resource_download/679

How do u feel about Trust there? Trust is the hardest to gain and the easist to go. Measure it somehow.. and start increasing mutual trust. Knowing each other helps. A lot.

the Lack of communication is the point of change. All else is not interesting. Analytics isn't going to change anything - u apply that to something that already works well, to measure and improve it. Yours doesnt work.
Accountability maybe, but if implemented without proper transparency and Trust, it will just turn people away (responsible but powerless).

so... as suggested. Start small. Have a look at organisational patterns book http://www.amazon.com/exec/obidos/tg/detail/-/0131467409/, print the most obviously missing/matching of them and "accidentaly" forget them by the printer or by some coworker (who u think might take it). Don't force it - try find allies in higher places.
Look at me site for more recomendations http://www.svilendobrev.com/rabota/ which although seemingly purely software, are more philosophical i.e. generic in nature.

Anyway, essentialy - do best u can, looking furthest u can. Don't micromanage in any way (analytics is such). And yes, Have fun.