Although you haven't given us a whole lot of information, it sounds like this bill has arisen because you haven't filed VAT & PAYE/PRSI returns for years in question. If this is the case, then you will need to have these returns prepared as a matter of urgency, and any liability paid also. Paying the bill in the absence of the return will get rid of this tax demand, but other demands will follow until and unless returns are filed. You will need to get proper accountancy advice, as a matter of urgency, as otherwise the whole issue could spiral out of your control unless handled properly.
The fact that the bills are in the name of a limited company that has "dissolved in debt" as you put it, is likely to seriously complicate matters, and there is a strong chance that the company directors could (1) be held personally liable for any unpaid debts to Revenue and third parties; (2) be subject to proceedings from the ODCE.