It isn't nice to hear, but your 533 has already exceeded its useful life expectancy by more than two years. Based on postings here and elsewhere and Pioneers internal info, most 533s died within 24 months of purchase. So, before going any further, take some comfort from the fact you got an exceptionally long run from a rather poory-designed recorder.
I am a heavy user of Pioneer DVD/HDD recorders, all models since the first one. They are all very good, some are really excellent, but the 531-533-633 of 2005 were a gigantic mis-step that nearly sank the company. That year, unlike Panasonic and Toshiba, Pioneer tried to add the TVGOS feature "on the cheap" by installing it as software on the HDD rather than as a dedicated hardware chip. This resulted in three incredibly unstable recorders subject to the vagaries of easily-corrupted, difficult to reinstall TV Guide software. When the Guide goes down, it takes the whole recorder with it, and its a huge PITA to repair. Its also very very difficult to determine whether a given problem is caused by TVGOS corruption, HDD failure, a worn-out DVD burner, or some combination of the three.
The first thing you should probably do is forget you ever heard of DL discs. For one, the 533 was never intended to burn them properly: the feature was a last-minute firmware change added to some but not all 533s. You are lucky it burned DL discs at all, never mind for five years- most 533s have terrible trouble handling DL. If you are using anything but Verbatim +R DL media, you are using garbage: the Verbatim +R DL is the only DL media that has proven reliable for DVD recorder use (PC burners will record to a frisbee or a coffee can lid- they can use any brand). The 533 is limited to -R DL, and -R DL has always been pretty awful.
The second thing you should do is try some TY/JVC 8x-speed premium DVD-R single-layer media: you can order it from supermediastore.com, rima.com and other web stores. This is the media your 533 was specifically designed to burn, its high-quality made-in-Japan stuff engineered especially for DVD recorders instead of PCs. If your 533 can finalize these discs, it still has some life left in it and has probably just lost the ability to cope with other media (TY/JVC also make the only good -R DL media, you could try that too). If your 533 can't finalize TY/JVC media, the burner may be shot or a problem in the HDD software is preventing the process from completing. You could search eBay and other sites for a good generic Pioneer DVR-109 burner that was sold for PCs, the same burner is used in the 533. Remove the burner from your 533, open both burners, and swap their green controller boards. Install the "new" burner in your 533, and it should work normally again. If it does not, mourn its passing and move on: the 533 is hell to fix, Pioneer is out of business, and the current Magnavox 513 DVD/HDD at Wal*Mart is a far better use of your money.