I'll explain how things work in big (Fortune 500) companies, smaller companies may conduct operations differently. When negotiating salary, most large firms have a rate sheet that tells them the median salary for each role. HR prefers to hire at a low number, so there's room for larger percentage increases in your annual review. The median is sometimes treated as the top hiring limit for the role. The hiring salary is super critical, because all of your raises will be based on a percentage increase from where you started. This is why it is generally advised to change jobs every two years, which can help to maximize your salary over time. Raises generally lag inflation (2-3%) for large companies.
The best opening response to the question of how much you want is, "I'm willing to accept market rates for the role. How much do you have budgeted for the position?" Most folks are surprisingly frank when you ask them straight up. I've had people lie to me (watch the body language) and I usually go very big if that happens - I probably don't want to work there, anyway. If they give you a number, you now have a salary floor to negotiate up.
I also like to defer the conversation until as late in the process as possible. This lets them fall in love with you and develop an emotional attachment, which makes it easier for them to make exceptions. So what I like to do, is to give them my budgeting line, and then say "...but we can finalize the details later."
Once you've maximized your salary ask, get more information on benefits. You can then get "soft comp" to subsidize your negotiated salary. Soft comp is stuff like 401k match (typically fixed, but sometimes you can get bumped into a better employee tier) life insurance, disability, cheaper health insurance, and (the big one) more vacation time. Some companies are more liberal than others on soft comp.
The reason you failed with your 100k ask is because you revealed your current salary. Never do that. It's a bad policy, but many large companies have strict limits on percentage increase from current salary they are allowed to provide, and once you provide this information, you can't take it back. A friend of mine in a tech support role took this advice and got a similar job for a competitor with over double the salary (he was dramatically underpaid).