DOORs is fairly straight forward to install. However, it is just a tool, and like any tool (particularly powerful ones), you need to not only learn to use it, you need to decide how you will use it, then everyone needs to learn to use it how you want it to be used. Then everyone needs to start using it, and (here's the really hard bit) do not stop using it.
If the cost of installing DOORs is a major concern, consider that it (and anything like it) might not be the correct product for you. Using DOORs effectively requires a very serious commitment to requirements and requirements management, from everyone involved in the SDLC. If you (and all the business) have not got that commitment, it will fail, and the cost of a few days, a server and maybe an IBM consultant pails into insignificance.
The fact that you "think you might have a license" indicates that someone in the past has toyed with the idea and failed. The fact you are concerned about the effort to install it, and as a software developer, would be maintaining it yourself, indicated you are toying with the idea. The word "I want" rather than "I am" is also a warning.
Perhaps you should come up with the requirements for your requirements management tool (using DOORs?).