The statute of limitations doesn't apply to the tickets themselves because the statute of limitations operates as a bar on prosecution after a certain amount of time. The way traffic tickets work, if you do not show up to court to contest the ticket, then a guilty judgment is entered against you. At that point, the prosecution is over and so the statute of limitations doesn't apply, because a judgment was already entered. I can't tell you why you haven't been contacted since then because the court or motor vehicles usually sends out something relating to it, but the fact that they didn't doesn't make the debt unlawful, because the citations
you receive tell you what will happen on the back. The courts do not often issue warrants when the ticket is a payable citation only (as opposed to a charge that carries jail time), but you may want to contact the clerk of court in Denton County to make sure that there isn't one out there to be certain if you aren't already.
It sounds like the state stopped trying to collect the fines and instead sold them to a debt collector. If that is the case, the statute of limitations on debt collection is 4 years and they are likely barred from suing you (but not for continuing to pursue the debt):
(The number for the Consumer Protection hotline is on that page as well and they are a good resource if you have further questions about the debt)
The main issue that might come up is that Texas does suspend licenses of individuals with unpaid tickets (it is an administrative penalty so no statute of limitations) so if you do choose not to pay the fines you may end up dealing with that at some point.