Shorter Answer
You are focusing on the trees and missing the forest.
Your best first step is to stop working for a place that hasn't paid you in weeks.
Indeed, anything you hear from the company about how they are going to fix the situation that is giving you the hope that is making you stay at your job at this point is more likely than not a straight out lie from management.
While your options are explored at greater length below, in all likelihood they aren't paying you because they don't have the money to pay you. If that is true, it is probably futile to even bring a lawsuit or have an agency intervene. How can you collect, if they are so broke that they can pay workers whom they'd like to keep for weeks?
Longer Answer
While in theory, the U.S. Department of Labor can bring suit against an employer that doesn't pay wages, on the theory that this violates the Fair Labor Standards Act minimum wage requirement, often it does not, in part, on the theory that the employer owes you at least the minimum wage, even if the employer hasn't paid it.
Also, usually the Department of Labor focuses its efforts on employers with lots of employees who are especially vulnerable and hence unable to look out for themselves, such as non-English speakers or developmentally disabled workers. So this makes it unlikely that they would take your case.
A minority of U.S. states have laws on the books that do provide far more effective remedies when wages aren't paid, either through agency action or a private lawsuit. But, without knowing which state you are in, it is impossible to determine if you could benefit from such a law.
The default and typical remedy, if you are not paid as agreed, is to bring a private lawsuit for payment of wages against your employer, because typically there is no agency willing to enforce a claim for unpaid wages.
Of course, if you have a contract with an arbitration clause with your employer, you must commence a private arbitration instead, and then bring a private lawsuit to enforce the arbitration awards.
Quite frankly, in your situation, being fired as retaliation is probably the least of your worries. Most people don't want to work for free and quit their job if their employer stops paying them.
Failure to make payroll is usually a strong sign that a company is extremely likely to file for bankruptcy and/or discontinue its operations imminently, often in a matter of days or a few weeks. Very few companies ever recover from that kind of situation.
Generally, you are best served by either quitting your job to cut your losses and suing for the wages you are owed, or not quitting and pressuring the employer without filing an agency complaint or lawsuit which could cause an employer to see you as an enemy to avoid paying instead of a friend to prioritize payment to. Quitting is a particularly attractive option in the current strong labor market.
Also, threatening to quit if you don't receive at least partial payment immediately and getting the employer to put the balance of its debt to you in writing, effectively confessing its liability, may be a good middle ground.
But, it rarely makes sense to file an agency complaint or lawsuit while still working there. The threat of a retaliation lawsuit is not very worrisome to a business that doesn't even have enough cash to make payroll anyway. It can't pay you money it doesn't have whether it owes you $5,000 of back wages or $500,000 of damages in a retaliation lawsuit.
Also, while small amounts of unpaid wages are entitled to preferential payment if the company goes bankrupt, the larger the debt that is owed to you for back wages is, the larger the share of that debt that will receive no preference vis-a-vis other creditors in a bankruptcy becomes. So, the bankruptcy code also encourages you to quit and find a new job in order to mitigate your damages when your employer fails to pay you for a sustained period of time.
