The real answer here is, as you stated, get a lawyer.
The second answer here is, what did you agree to when you formed the partnership? Do you have any documents that say how to dissolve it? Or what to do when somebody wants out? You'll need to follow those rules. And a lawyer will walk you through that and any other financial and legal obligations that you might need to work through, based on your partnership agreement and the local laws.
But supposing you don't have anything along those lines...
I personally love the concept of a shotgun clause. Any potential profit-earning endeavor I do, I try to put one in.
It's basically the same as the idea of cake cutting, where one person can cut the cake, and the other person gets to choose which half they want. It ensures that the first person doesn't cut the cake unfairly, because they don't know which half they'll end up with.
With a shotgun clause, the person who invokes the clause gets to name the price per share, and the other person gets to decide whether they sell their shares to the other, or buy the shares from the other. It's not a perfect system, but it does solve a lot of problems.
If your partner isn't willing to sell out for less than $100,000, then that would assume that's how much he values half the company. It would follow that he's willing to buy for that much too. Start by telling him that the partnership is over, and that since he is valuing his shares at > $100,000, that you will sell yours to him for that much.
He's likely to say that he won't do that, but it might get him to realize he needs to be reasonable. Whether you signed an agreement that included a shotgun clause or not, you might be able to get him to agree that it's a fair way to terminate the partnership.