I received a seatbelt ticket in NYS (I'm licensed in NJ). I went online to answer the ticket, put in my personal information, but the system has no record of a ticket being entered in my name. It's been almost a week since I received the ticket. Does this mean that they somehow overlooked, or possibly got my information wrong, so that I can forget about this nonsense?

Its not nonsense. It may take a while to post the ticket. There may be a contact e-mail on the website where you can check on the status,

Its not nonsense. It may take a while to post the ticket. There may be a contact e-mail on the website where you can check on the status,

The ticket says I have 15 days to respond, otherwise they will suspend my license etc. What happens if they don't enter the ticket into the system within 15 days, thus making it impossible for me to respond?

Print out the message showing that it wasn't entered.

Make sure you are entering the info exactly as on the ticket.

The ticket says I have 15 days to respond, otherwise they will suspend my license etc. What happens if they don't enter the ticket into the system within 15 days, thus making it impossible for me to respond?

If they don't enter the ticket in the system, they would have to process it the old fashioned way- in the court clerk's office. I don't see that happening. So, as ScottGem said, contact them by phone and find out what the problem is.

Yes with cut backs and the such, it may take 2 or 3 weeks for tickets to show up, Even in my local area I never have seen a ticket make it into the system in one week.

So you need to follow up on this in other methods given