You voluntarily quit one job. You left it to go to another job, and worked one week. Then you were "let go" in other words, terminated from the last job. When your claim was set up, by law, it was based on the first four of the last five completed quarters. Right now, if it was set up in March, 2012, it would be based on the wages you made, in other words, from Oct. 2010 through Sept. 2011. Your last employer had no liability for wages paid to you, it would all fall back on your next to last, long term employer. You quit the job with them. A person who voluntarily quits a job, without a very excellent job related reason to quit (such as not being paid, or being forced to work in unsafe conditions) is not eligible for unemployment benefits. This is the case whether or not the employer "fights" the claim or not. All that has to be determined is that you quit them. That means you get no unemployment if you did not have a good reason to quit.
It is not, incidentally, decided by "the courts". It is decided by the state unemployment system. You file the claim, as you have, and you will receive a notice of approval or denial within a few weeks. You can then appeal the decision if denied, but if you aren't able to present much of a good reason,that's going to cause a problem. You may be able to say you quit the job to take this new job, which you assumed was going to be permanent full time employment elsewhere, ( and which might be considered a valid reason to leave the old job) then you did the new job to the best of your abilities, but were let go after the first week. This may get you eligible for unemployment insurance. What will happen is that your previous employer, the one you quit, will request and very well may receive a non-charge to their tax account, if you are approved to receive benefits. This is fair, and this is something you do not have to worry about either way. You're still being paid, the money is just coming from a different place.
This law is set up this way so that you can't work at a job for a long time, then get fired or quit and go to work for your uncle Joe down at the filling station and get a lay off slip after three days and begin drawing unemployment, which will all come from the account of your previous employer, not Uncle Joe's account. In order to be able to draw from the last employer, you must have a minimum amount of earnings from them.
If you do not, and you are laid off after a very short time for a valid no fault reason, or were terminated and they cannot show job related misconduct, you may still be able to draw and your old employer not be penalized. File those appeals. It costs nothing, and is worth a shot while you are looking for a new job.
