I strongly advise you to keep the job, and start looking for another one while you are still working. Because I don't know how long you've been there, and I don't know how much you make, but for the most part, unemployment insurance IF it were to be approved for this quit, would be much less than you could make working, even with a 4 dollar an hour reduction in your pay.
It would take a long time to get it approved even if it is and unlike Chyvan, I do not think you have a whole lot to work with regarding getting approved. It is what it is. You quit due to a demotion. The demotion was a result of disciplinary actions being taken against you. That's a big kettle of fish, and would take as much as a couple of months to fry out in the unemployment appeals process. If you are approved, you'd be backpaid for the weeks since you filed as long as you have made certifications for them, eventually. But it's not a sure thing you'd be approved by any means, and like I said, it's a long time without anything at all coming in.
If you quit your job in this circumstance, they do not look at it as being that the employer fired you from one job and offered you another. The employer is always free to change his employees hours and shifts and pay rates without sanction "for the good of the business." They do not have to prove you had actual misconduct before they can change your job assignment, mess with your shifts or cut your pay.
It's just going to come down to that they, for disciplinary reasons, decided to demote you, cut your pay based on the demotion, and change your shift as the new job required a different shift. You decided not to accept this change, but to quit the job instead. The burden of proof that you had a valid reason to quit the job is on you all the way here.
And then, if best case scenario, you got approved for unemployment, you'd have to be looking for another job like crazy anyhow, because at the end of 26 weeks or sometimes less, no more at the present time without federal extensions, you'd be out of unemployment benefits. This is regardless of whether or not you still need them, haven't found another good job yet. The most you could draw a week is somewhere in the neighborhood of $650 a week for 26 weeks. Then it stops.
Take your time to "explore the labor market" and see if you can replace this job where they have done you wrong without quitting. That's my best advice when I look at this.
I agree, if you are going to quit rather than take the demotion, then do not work even one minute at the new rate and the new job. If you do, then that is considered your new position, regardless of how long you've worked it, and your pay rate is the rate of the new job, and you don't have a prayer of being approved for unemployment if you quit it because you are making less than you were before.
When a person quits their job, in unemployment insurance, the burden of proof is upon them. They must show they had a valid job related reason to quit the job. A dramatic reduction in hours or pay, especially if it causes the loss of benefits and is obviously done in an attempt to get the person to quit, is the best case scenario for being approved when quitting the job.
Technically there is no absolute threshold where if it's 20% of your former wages you'd still be making or less you can quit it and be approved but if it's 21% you can't be approved. That's just a sort of guideline, but a lot of other factors are considered, as well.
But a warning here. Changing your shift, which does not agree without your own personal schedule is not really one of those things they look at. And they're not going to be terribly sympathetic about your losing the shift it was most convenient for you to work, particularly in a situation where your changes were related to discipline, so don't count on that being a factor in your approval or denial.