Should I shut down my company

Get another investor to by them out. Let them know they either take it or you shut the company down.

If the investor isn't giving connections or anything else of value, how is the investor still involved? If they just have equity in your startup and let you do your own thing, that's not so bad. If they're a minority shareholder you can just ignore them and focus on your business. If you're sore about the investor having equity without doing any work, then you need to grow up.

An investor doesn't care about 25k, so they also won't care about your startup. They invest in 25k in 100 startups, hoping one of them becomes a unicorn. If your startup isn't a unicorn, they don't care about you.

If you shut down your company you can't take any of the IP with you for a new venture. That will set you back enormously. It doesn't make sense to give up if your startup is showing promise.

If the investor is inexperienced, you may be able to dilute them or otherwise screw them out of their shares. Once you're making good money you can probably afford to have some lawyers explore the options. For the time being you better just suck it up and grow your business.

Sometimes you jump into bed with the devil. You did, most likely because you wanted Money. If they are doing nothing then buy them out, but wait, do you actually have any money coming in? Next time do your due diligence.

There are good failures and bad failures. This would be a bad failure. It should be reflected on both your score cards much like a credit rating.

If I had a founder that I funded quit that easily, they should not be allowed to get back on the horse anytime soon, if at all.

The ex-founder should steer unwitting entrepreneurs away from said investor/accelerated if they believe that the experience was not unique to themselves.