Yes, a former employee can proceed under PAGA. However, to proceed under PAGA, you are supposed to serve a "PAGA notice" within one year of the violation you are claiming. You serve a certified letter on the Defendant and the Labor and Workforce Development Agency at:
California Labor & Workforce Development Agency
800 Capitol Mall, MIC-55
Sacramento, CA 95814
You are probably too late. You can also file a wage claim with the Division of Labor Standards Enforcement and some of the limitations periods are longer, but you will not be eligible for PAGA penalties that way. (See http://www.dir.ca.gov/dlse/HowToFileWageClaim.htm for more details).
As a general piece of legal advice, if you ever feel like your rights are violated you should consult with a lawyer about your options immediately. Waiting four years is a very bad idea, as most statute(s) of limitation have run by then. The shortest statutes of limitation are six months, so moving quickly really is critical to preserving your rights.
With all that being said, there are sometimes arguments you can make for "tolling" the limitations period, which basically means that you argue the statute of limitations was not running for some period of time. The argument can be based on a lot of things, but most often it arises when the Defendant has caused you to miss the statute of limitations, such as pretending to negotiate a settlement with you and walking away from negotiations right after the statute of limitations expires.
You should consult with a local employment lawyer right away to see if you have any tolling argument to be made, whether they are interested in your UCL claim even if PAGA is not available, etc.
Best of luck to you.
The information provided in this Answer is offered for educational purposes only and should not be construed as legal advice or counseling. You should not rely on the information herein in assessing your legal rights, determining to take legal action, in any formal papers filed in a legal or administrative forum, or in any way whatsoever. Moreover, this Answer does not create an attorney-client relationship - only the formal, written agreement required by the State Bar of California can do that. You should always have a full consultation with a lawyer if you are contemplating any sort of legal action.
For wage-and-hour violations premised on the Labor Code, the statute of limitations is three years. Thus, you can collect the actual wages owed plus any statutory penalties on wages that were earned but not paid within the past three years. By asserting a UCL claim, you can recover a fourth year of wages, but not any statutory penalties on that fourth year of wages.
The UCL claim thus allows a plaintiff to get unpaid wages more than three years old that would be time barred under a standard Labor Code wage-and-hour lawsuit. The UCL claim additionally allows a plaintiff to determine if there were other employees who were similarly not paid as part of the employer's business practice. The plaintiff can get an order under the UCL ordering that the employer pay those unpaid wages to all of those other employees, again, subject to the four-year statute of limitations.
It sounds like, however, that you may not have any unpaid wage claim within even the UCL's longer four-year period. If you quit your job more than four years ago, all of your unpaid wage claims would be time barred, unless you can show some equitable reason why the limitations period should have been tolled (e.g., your employer lied to you to keep you from filing a lawsuit, and you were reasonable in relying upon that lie in not filing a lawsuit). If you quit your job just under four years ago, then your recovery of wages would be limited to whatever wages you earned within the past four years.
In your circumstances, even if there were not statute of limitations issues on a PAGA claim, a PAGA claim doesn't really get you anything of personal benefit additional to what you could get under a UCL claim.