My fan connector broke loose when disassembling my PS3 slim (CECH2004A). Might be my fault but I’m pretty sure Sony purposely built a fairly fragile part there, as the rest of the connectors are quite solid (and Sony aren’t renown for openness). Luckily the PS3 (this very model, at least) still accepts to boot even without a fan, so it’s an easy hack to connect an external power supply to the fan. An old 5v power supply (usb charger) did the trick. Simply conect the fan’s negative wire (black) to the charger’s negative wire and the other two to the charger’s positive wire. There’s also enough space to drill a small hole for the cable near the power plug.
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The downside is the fan is on all the time so it’s a bit noisy and it might reduce your fan’s lifespan but it’s a very easy hack to keep your PS3 alive.
See https://www.youtube.com/watch?v=6SXydvxnYpE (not my video but the exact same trick)