@IICaRBiNeII heya
You can see if they are on your account by logging in to the Origin client and going to your games library. If the game shows up there, then it is registered. All you need to do then is install the Origin client ( http://origin.com/download ) on your new laptop and install the game. You can then follow @EA_Kristi's instructions as to copy over your saves.
If you do not see the game in your games library, then you can register the games. To do so: open up the Origin client (doesn't matter which laptop - it's just your account we're registering the game on, not the laptop) and click on the "games" button at the top and choose "redeem product code." Then redeem all your games and they'll be registered.
If you don't have your codes, then you can find them through the registry:
You need to be signed in as an Administrator first. Windows may require your permission to open the
Registry Editor and if so, just click on yes.
Press the Windows key on your keyboard and type regedit in the search bar and press Enter.
Click on 'File' at the top left of the window that opens then click on Export.
Choose a location and name for the file as this will be your backup registry file.
Click Save.
This backup is created just as a precaution.
Now to find your serial codes for each specific EP or SP installed on your computer:
Expand the HKEY_LOCAL_MACHINE folder.
Expand the SOFTWARE folder (Wow6432Node for 64 bit systems)
Expand the Electronic Arts folder.
Expand the Sims folder
Expand the EP or SP you need the code for
Click on ergc and in the box to the right under 'Data' you will see the code
Write it down somewhere safe
Repeat above steps for each EP
Again, once you've found them - you can redeem them on Origin.
Let me know if this makes sense and helps!