In general, medication should not be used past the expiration date. There is no guarantee that the DayQuil can still be considered safe and effective, especially that long after expiration. Medication begins to lose its potency over time. This means the medication may not work like it is supposed to. It is much better to be on the safe side and not take expired medication.
The FDA has a special publication that addresses the question of using expired medication. It is the FDA's position also that taking expired medications is not worth the risk. It cannot be determined that the medication in question will still work as it was intended. Furthermore, having expired medication in the house potentially poses a risk to children and pets if accidentally ingested. It is much better to dispose of the medication properly once the therapy is completed or the medication expires.
While a medication may "look okay", the possibility exists that there could be bacterial growth. Medications improperly stored in hot, damp places can also lead to problems of stability of the medication. It is best to store medications in a cool, dry place or as indicated on the prescription to preserve the effectiveness of the medication until the expiration date.
While it may be tempting to take the expired DayQuil, it is much safer if a new bottle is bought. Taking expired medication is an unknown risk that should not be taken.