You have two different questions here:
1) Can quantum computing be profitable without quantum hardware?
In the comments people have said this is an opinion based question, but the truth is that there's already people (and companies!) making profits off of quantum computing.
In 2016 Doug Finke made a website with his own money, which kept track of the number of qubits in all quantum computers, and a list of all companies involved in quantum computing. In 2018 started making profit from advertising. Recently he has also added a job postings section where Google, IBM, Microsoft, and other big companies have job openings listed there. He now makes even more money from consulting. Although it might sound like it, I am in no way related to the person or website, he just attends some of the major quantum computing conferences and makes himself known.
There's more than just individual consultants making profits off of quantum computing. A famous quantum information theorist (Michele Mosca) and famous a physicist known for his work in quantum key distribution (Norbert Lutkenhaus) started a company called evolutionQ which makes a profit by selling products (if you click the link a PDF will open) such as courses on quantum-safe security, and quantum cryptography, and for other products like risk assessments and even software. Again, I have no relation to this company.
So far I've given an example of an individual person making profit from advertising on a website about quantum computers, and a company making a profit from consulting about quantum computing. If you are very picky you might say that these are not examples of quantum computing being profitale without hardware, because no quantum computing is actually directly involved. So I will give a third example:
The company 1Qbit is a company that does not have any quantum hardware, but thrives by making algorithms and software for companies that are interested in running things on present or future quantum hardware. Again, I have no relation to this company.
How long will the above three examples keep making profit?
That is what is opinion based.
Some people (not necessarily me) are of the opinion that quantum computers that can actually outperform classical computers for a useful task will never exist, so eventually people will get less and less interested in spending money on advertising on a QC-related website, or on buying software for present or future quantum computers, or on consulting fees or courses. Others disagree and think that quantum computing will become an industry just like classical computing (i.e. profits can be made by plenty of companies that don't have hardware, such as software companies, consulting companies, magazine publishers, etc.).
2) What are the fields/business ideas that a new business can work on within quantum computing that can be profitable if this business has no access to onboard quantum setups but can access the cloud-based quantum computing platforms?
This is a different question.
First, if you have access to cloud-based quantum hardware, you can run calculations on the hardware, just like if you had it yourself in front of you, so your potential to make profit can't be too much smaller than if you actually had the hardware in front of you. Maybe you just want to know if people can make a profit apart from selling hardware? Selling the hardware is probably the only thing that you can't do to make profit if you only have access to the cloud-based hardware.
If you want to know how you can make profit from quantum computing is some way other than selling hardware, there some "fields" (as you call them) in which this can be done. Some examples are consulting, software development, algorithm development, and teaching private courses.
In terms of actually using the cloud-based quantum hardware to make profit, your chances of making a profit are smaller. Nothing useful that a cloud-based quantum computer can do at present cannot already be done for less cost on a classical computer (though companies like IBM are known to offer their cloud-based QPU time for free, there is still not much you can do to make money from running calculations on their cloud based chips because they don't have enough qubits to do anything very useful). You would have to be extremely good at sales to make a profit right now, and whether or not you will be able to do it easier in the future is an opinion-based matter. Present-day hardware (whether available on the cloud or not) is mainly only useful for testing the physics of the chips, or for playing around. If a competing company needs someone to learn how IBM's chip works for example, maybe they could pay you to do some experiments, but they probably already have someone that can do it. Maybe you can organize games, tournaments, or other prized competitions for doing small calculations on present-day devices and get sponsors for that, but that is about it!