Your mistake was not to file for unemployment benefits immediately on leaving the old job. At that point, since you were out of work through no fault of your own, you'd have had what's called a "clean claim." Your separating employer would have been the one where you were making $70,000 a year.
Even if you didn't "need" them, because you were receiving severance, or because you thought you'd be able to walk into something else immediately, you should have filed for them during the first week you were not working. Waiting until you were really frightened, till you'd discovered there weren't a lot of good jobs out there to find quickly was a bad idea. If you'd called the unemployment system they'd have advised you to sign up. I used to work with plant and business closures, and this was something we always counseled people to do, even if they were sure they had another job to go to very soon.
If you wait long enough, there will not be any money for you to draw, either. Unemployment is based on your employment record during the first four of the last five completed quarters. If you wait six months or a year after you have been laid off to apply for it, you will have a lot less money, or no money at all in those quarters that are used, and often will not have a claim at all. It doesn't matter that you'd been gainfully employed for the last thirty years. It is only based on the last few quarters, and they roll forward each time the quarter changes. So a blank spot in your work history, even though you were searching diligently for jobs during that time, may mean no unemployment eligibility.
Many people have this misconception, that unemployment is a "needs based" welfare type program using the taxpayer's money (wrong!) and that they shouldn't file for it until they are truly desperate. They also believe, while working, that the economy is better than it is, and that people who are not working are doing so because they enjoy the luxurious amount of money they're getting on unemployment and don't really want a job.
Reality sets in quickly. It takes, under the best of circumstances, three to four weeks to get unemployment benefits going after you file for them. If the separation issues are disputed, it may take longer. In order to be eligible for each week's unemployment check, you must be able, available and actively seeking equivalent work. Equivalent means similar in nature and pay to what your separating employment was. As they always explained it, the definition of "equivalent" changes gradually over the weeks of your regular claim (which is never more than 26 weeks maximum).
But in any case, it's a moot point because you made a poor decision, as you said, in panic mode, and accepted another job. Even if you had decided to accept a fast food cashier job, as long as you are making more in gross pay in a Sunday through Saturday week at this job than your weekly unemployment benefit would be, this job is going to be your separating employer if you decide to quit and reopen your unemployment claim.
When you accepted the job, it is understood that you accepted the conditions and terms of the job. If you then quit the job, stating that you are not making as much money as you were at your former job, you have a very very little, slim to none chance that you would be approved for unemployment benefits. In order to be approved when you have quit a job, any job, even if it is not suitable for you or similar to your past jobs, you must show you had a valid work related reason to quit the job. If you went into it knowing what the job paid and what you would be doing there, then in most cases, you do not have a valid reason to quit for unemployment purposes.
If they had lied to you and told you to expect $70,000 a year, and then you found out once you were there that they were only going to pay you $30,000 a year, that might be considered a good reason to quit, and you might actually have a chance to draw benefits. But even if approved, this would be your separating employer now, so you couldn't demand a job paying what you made on your previous job, even for a few weeks.
So I'd advise you to begin an arduous search for a better paying job WHILE you are working at this one. After all, you are making quite a bit more right now than you would be making while drawing unemployment benefits anyway, even though it is much less than you used to make. If you were to be terminated from this job, you might have a fairly good chance of being approved for benefits, as long as you were not terminated for work related misconduct. If you show up and do your best every day, and the employer still decides to let you go after your first few weeks or months on the job, due to "poor performance" or a "bad fit" or something similar, then you'd likely be able to get approved for unemployment benefits. But if you do the driving in this, if you up and quit the job, then your chances of getting back on unemployment are very small.
Even if you hadn't taken this job, you would still, by now, be having to consider jobs that paid less. And ignorance of how the unemployment system works is not ever an excuse that would allow you a do-over. As we said, it's not needs based, you do not get approved for it because you are poor or desperate. It's an insurance program, it's paid in by the employers of your state, signing up for it is voluntary, and you qualify for it or you do not, based on your work record with all previous covered employers. It has nothing to do with your need or level of desperation. And the explanations of how the program works, in every state, are pretty much available to everyone who looks for answers.