I have been in the position of starting a venture like this and I know how the beginners feel:

- how do I get leads?
- I don't have a budget for this.
- what software should I be using?
- I have the contact, but they do not answer on LinkedIn. What do I do?

Use ContactOut (https://contactout.com). It is the best and smoothest software I found for sourcing emails and telephone numbers.
It also gives you 40 free leads every month so you can test it out.