I have a computer constantly connected to the network with free electricity. Of course, I could mine, but I have outdated hardware + I don't like the idea of meaningless calculations.
I want, without investing my own funds, to support the ecosystem of any coin and receive currency for it. For example, my computer can contain the entire blockchain, verifying the history and current operations, saving the network from an attack of 51%.
Please, tell me about similar coins.
There is no free lunch. You can't expect to get something without giving something.
One of the cheapest option I can suggest you is to run Horizen Secure Node. Check here for more information
https://www.horizen.global/securenodes/. While Super Node requires 500 ZEN, Secure Node require just 42 ZEN.