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Try starting your game without Origins using "C:\Program Files (x86)\Origin Games\The Sims 2 Ultimate Collection\Fun with Pets\SP9\TSBin\Sims2EP9.exe". If the problem is Origins-related, this should fix it.
Eh, Origin may still think your "old" computer is a separate machine that still exists and has the game installed on it. I imagine the simplest solution is to contact EA CS and explain what happened. There's a bug with TS3 that causes this error, so they may well have messed it up in the same way for UC.
What I lack in decorum, I make up for with an absence of tact.