Installing the Sims 3 from Origin onto new laptop without disc available

[kristenbianca]

I'm trying to install my Sims 3 base game, expansions and stuff packs from Origin onto a new laptop but I do not have  my discs available.  I clicked "download" on the base game first... took three hours to download, then when i entered the product key (which is shown in the "i" screen in the Origin client) it said the product key was not valid.  Not sure what to do at this point... any suggestions?