I just got married and have not filed for an AOS yet. I found out that my current employer is going out of business and I'll need to find a new job. Can I apply for a new TN if I have not filed an AOS yet?

I don't know what TN stands for, but if you're currently work authorized (e.g. if you got the work authorization stamp upon entry into the country), you're allowed to work until your I-94 expires (90 days after your entry). It would be wise to file for AOS and EAD as soon as possible, still. After the 90 days, well, you can't technically work, but if you've already been hired and are working, then it's the employer's problem to make sure you still are allowed to work, and since you should be married to a US citizen at that point, USCIS will forgive you if they learn about it.

Me either

TN is temporary national. It allows me to work for a single company for up to a year at a time. It also specifies that I can't establish permanent intent.

Methinks not. Maybe you should read the instructions for the TN visa, see if it says anything about restrictions and/or make an infopass appointment with your local office to ask this if it isn't clear. Hopefully someone will be along later that can help you.

Wouldn't let me edit my previous post, but here's what I found regarding the TN Visa:

http://www.northwestern.edu/international/...ctions_link.pdf

Down the page a bit it says what the requirements are:

Eligibility Requirements:
Must be Canadian Citizen
Possess the minimum qualifications as per the designated occupation
Credentials must have been earned from institutions located in Canada or the United States
Evaluations of credentials if degree earned from institutions outside Canada or the U.S.
Applicant must possess any required license to perform the duties
Employment must be temporary
Department of Labor (DOL) certification not required
No prior petition need be filed
Non-immigrant intent

I think you would be safer to file the AOS asap. With the TN, you will be out of status when you lose your current job.
It would also be kind of risky to go to a POE to get a new TN; if they find out you are married to a USC, it is usually considered immigrant intent. The other alternative is to do the new Tn by mail, but that would probably take almost as long as getting the EAD.