Finding appropriate sponsors is hard. Let me tell you something first: in your case, you don't approach companies, you approach local companies.
Events with 2000 participants are events which are widely known. People come together and gather even if they travel for 12 hours or more. Some of these events are probably so big that there even is a live-stream, an after party or a documentation uploaded to YouTube. The difference between a large-scale event and a local community gathering is clear: less people, less opportunity to promote.
If we talk about the TI (The International, a esport event for Dota 2), the LoL World Championships (a large-scale event for the League of Legends) or a Champions League match, sponsors will come to you to ask for a place to promote or if they can support you. They know that people will recognize their name. "Oh, didn't company X support the last event?" "Yes, nice of them!"
Your event is small-scale even if you already have 70+ participants, it's most likely not attractive for big companies to support you. But, it never hurts to ask for assistance. There are big companies who are interested in helping you, however, most of the times some other small events already claimed help and the big company isn't up to helping everybody. This means that you should ask for support really early on. A company has limited resources and these may be gone if you ask too late.
If you decide to ask for assistance of a big corporation, make sure to offer them something in return (there aren't many corporations who will help you for the sake of good will):
- the name of the company is on your invitation letter
- a booth where you sell products (merch, drinks, food)
- a program on your stage to promote their products
- the opportunity to film a promotion video with your participants
- offer them the opportunity to design the project with you
These are some ideas to appeal companies. Especially the last one could get you a sponsorship. A sponsorship is a great promotion, a partnership is even better. (But this can be become ugly if your ideas collide with the ideas of the company, especially if it's a partnership. It could happen that you have to accept what they want since they have the money.)
Don't be disappointed if there are no global companies who wish to help you. A LAN event isn't just about gaming, it's about being together and having fun while playing. You have to have place to rest, eat, and drink. Approach local shops and companies to lower the cost of all these side things. Ask a bakery for buns, ask a grocery store for drinks and other food, ask a distillery for alcohol. Local companies are happy to help you, it makes their name more shiny. (You can also think about program for the evening, like a show or something and ask local groups to perform.)
Nevertheless, there are things to consider if you're asking local shops. You don't need to ask for support of these who don't provide anything crucial for your community gathering. Why would a clothing store support you? Do you sell jeans? Why would a florist help you? Do you sell roses? You see, no need to ask for support of these who can't fulfill the needs of your participants.
When people ask for support, companies think of it:
- If I help there, what is the gain of it?
- Are the people attending my audience?
- Can the organizer cooperate with me?
- Has it had success in the past?
I'm pretty sure that a church isn't that ready to help you as a local fast food shop is because...
- ... the most attending people are the audience of the fast food shop.
- ... your goal is to satisfy the need of the audience by providing food.
- ... you are willing to cooperate to satisfy the needs of your audience.
- ... you had success in the past and sold a lot of fast food and snacks.
However, always keep in mind that there are some companies who need to improve their reputation and will do things for less. That's the reason why it never hurts to ask big companies if they haven't explicitly denied support in the past.
- Ask big companies earlier on, at least nine months, a year is even better.
- Ask local shops and companies to help you to cover the basic needs.
- If financial supports is needed, don't hesitate to ask local credit institutions.
- If you are part of a (state) organization, ask for assistance carrying out the event.