I run bitmonerod on my laptop when I'm using the computer but I shut it down for the night. I don't mine due to the computer relatively low capabilities.
How useful for the whole Monero network is a full node that does not mine and that is active only part of the day?
First and foremost, any node run from home, i.e., run on your own personal computer contributes significantly to the decentralization of the network. Ideally, to decentralize hashing power, such a node would also mine. In the future Monero will hopefully maintain decentralization in both hashing power and full nodes.
To answer your question, a node that is only partially online (i.e. only during the day), also benefits the Monero network and its decentralization. Although a node that does not mine is, alas, unable to contribute to the decentralization in hashing power. I'd argue that there is a linear relationship between the amount of hours that the node is online and the usefulness to the Monero network and its decentralization, conditional on the node properties being the same. Bear in mind that running a full node in Monero actually has an incentive, namely privacy. That is, running a full node will give you the greatest privacy in Monero. By contrast, using a remote node via, for instance, a lightweight client is actually detrimental to privacy. In addition, the difference in privacy between a full node/client and a lightweight client is significantly greater in Monero than in Bitcoin.
