This exact scenario happened to me on I-95 in Philadelphia during a busy time some years ago. I was the second in line in the merging lane, with a decent amount of space between me and the car in front of me. The car in front never made an attempt to merge onto the main highway, and continued to go straight, decelerating. The merging lane was ending, so they were heading into the shoulder.

There were many cars on the main highway and no one was letting me in. In a normal situation, I would accelerate or stay in the merging lane, but the the car in front of me was slowing down and not merging. In addition, there were many cars behind me, expecting me to merge.

The gap between me and the car in front of me was closing. I spent some more time in the merging lane, waiting to see what the car in front of me would do (they did nothing and decelerated straight), before flooring the gas and merging in front of the cars to the left of me. Horns immediately blared, but thank God I made the maneuver with enough room to spare. I didn't have the awareness to see what happened to the car in front of me.

My parents were in the car, and my dad immediately started criticizing me for making such a risky play. I had been driving for ~10 years at that point, and I had never encountered that situation in my life, with mere seconds to make a decision. He said I should have decelerated behind that car and went into the shoulder lane behind him, which would have avoided me having to accelerate and merge into the left lane. This logic makes sense to me, but 1) that maneuver also invites risk and 2) wasn't obvious given the mere seconds to spare, poor behavior of other drivers, and novelty of the situation.

TLDR; you are merging onto a busy freeway sandwiched between a non-merging car and people behind you. No one is letting you in. What do you do?