
If you have a Mac there may be some similar software but I am not sure. It is trial ware that will work for a few days which should be long enough to get your serial number assuming you've never installed it before: Products: Belarc Advisor

If the computer being replaced is a PC and you can still run software on it then download and run the Belarc Advisor and it can find your serial number in it's report of software on your computer. Boxed software from somewhere else won't be listed in the orders but if you registered it should still be listed in the Products area.

There should be both a Products and Order History section, where Products shows all the serial numbers and Order History shows the orders you've made through directly. If you registered your Elements with an AdobeID then will have a record of the serial number that you can see by logging in with the AdobeID you registered the product using, click on manage account and then Plans and Products across the top.

I think the 9 digit number is just some printing sequence for the label or maybe a product number so won't do you any good. A PSE serial number is 6 groups of 4 digits with the first four digits being 1057.
