Most slim PS3s can be jailbroken, up to certain 25xxx models. Later models (30xxx and beyond) cannot be jailbroken - only HEN is compatible with those.
See Coro's jailbreaking guide for instructions on using bguerville's PS3 Toolset which will let you know if your PS3 can be jailbroken or not. If it's compatible, you can then install a noBT CFW which is made specifically for consoles with a broken Bluetooth/WiFi module..
CFW 4.90 Evilnat Cobra thread - scroll down to the download links and you will see the noBT option.
CFW Evilnat 4.90 Cobra 8.4 [CEX] [noBT] is the version I would suggest to install. Hope this helps.