You should really have your 533 looked at by an independent repair shop, unlike Pioneer service centers the independents will usually confine their repair attempts to the obvious simple problem, which is most likely a bad solder joint from motherboard to video out jacks. This is a fairly common electronics repair task and shouldn't be too expensive, and again unlike Pioneer the independent guy won't tamper with the HDD. There's a good chance you have an under-$100 repair problem here. I would go this route before attempting anything more drastic like transplanting the drive into another recorder (the cost of a "generic" service remote knockoff alone exceeds $50, plus you have get the two discs).
Note transplanting drives between various models can be unpredictable: sometimes the donor chassis easily accepts the HDD and lets you offload the videos, sometimes not. I have succeeded in doing this among the 510, 520, 540 and 640 models but have not tried it using an HDD from a 531-533-633. Again, the 2005 Pioneers were kind of a one-off, bizarro-world anomaly among Pioneer recorders: they have an added layer of complex software interactions due to the TVGOS feature. It is difficult enough to get a 533 to accept another HDD, theres no telling how its eccentric HDD software would affect an interchange to another model altogether. A 520 might ignore the TVGOS software and just read the video files, or the TVGOS software might confuse or lock out the 520 operating system. And the 533 does not take kindly to having either its burner or HDD removed and replaced: you may not be able to put the 533 back together into a functional unit.
If your 533 burner and HDD were working OK before this video output problem, its worth putting $100 into it to get it fixed professionally. If your burner and HDD were working normally, and this is just a broken connection in the video outputs, the recorder can and should be fixed. OTOH, if you were also having any burner or HDD issues, those usually cannot be repaired in a 533 and the machine should be discarded or sold off "as-is". Buy a new Magnavox H2160 from Wal*Mart online ($198) or J&R Electronics (refurbished like new $159). The H2160 has comparable features/performance but includes an ATSC tuner and is easily DIY repaired.