$0/revenue means every $1 in price has to be justified by something that is not your time.

Do you have users now, just non-paying? How many users? Do you have a monetization strategy? Have you tested if people will pay for it? Have you tested price points to value your customers? Without any of that, in my experience you are looking at more like $1-5k with every dollar having to be justified by something other than your time or you having hired a designer to do some work for you.

There are of course exceptions, and I mean no offense, it is just the economics of how deals work. Your time in design & development won't justify much of a sales price without you having proven there is a market and opportunity.

Now, you know you have spent a lot of hours on building your project which means it's likely you solved some problems that other people with similar interests and projects may have faced or are still facing. If you already have a solution for for a problem, try selling it.

If you aren't able to sell it and If open sourcing is possible for that part of your codebase that solves a problem then you could try getting sponsors/donations/etc and GitHub recently introduced that. This will allow you to showcase your skills and worth for your "code". I say "code" because that's all that it is to me. I don't know what it does, I don't know how maintainable it is, I don't know if it's well tested. It's very hard to sell just "code" based on "work hours".

Now using this approach, you might just be able to establish some worth for your whole project by advertising it as, Uses the popular, scalable and battle tested "your open sourced code" - also by me

Now I'm not sure how useful these things might be to you. Just my two cents. Good luck.

I am intensely curious to what would make a website worth "at least" $10,000 while generating no revenue and is not being actively used. Is it just the name that's worth the money? If so, I fail to see the significance of dev and design time.

Do you have a specific target market for the website? What would a potential buyer of your website be looking for, such that when they came across your website they said "that checks all the boxes"? (and, presumably, they would be saying "holy smokes that'll save us 10's of thousands in design time!")

Without revenue, what are you offering beyond "a website"? In the case that you have set a realistic price, were you as terse with your description of the website while trying to sell on Flippa?

Is it a side project with a validated market that you've built a prototype for but don't have customers?

When attempting to sell a side project, there usually needs to be indications that it will return some money at some point.