Greetings, and welcome to CDFreaks! Glad you could join us!
First, looking at the model number for the discs that you posted, it seems to correspond to some very old Pioneer 2x DVD-R media. One of the problems with using media that old in a more modern burner is that proper support for it may not be present in the burner’s firmware, and consequently, you may have problems using it, as you have experienced. You see, over time, as newer burners have been introduced and older media has been discontinued, many manufacturers have removed support for that older media from their firmware. In particular, many modern burners may have difficulty burning older 1x, 2x, and 4x media. One solution to this problem would be to use the media in an older 8x, 4x, or 2x burner, which is more likely to have support for it than a modern 16x, 18x, 20x, or 22x burner.
Second, the burner that you have, the Philips DVD8631, may actually function better if you were to do something that people around here call cross-flashing. You see, the DVD8631 is also known by another name, the BenQ DW1620, and sometimes (but not always), when you convert a drive into it’s other persona using a firmware cross-flash, the drive can work better and some technical problems that may have afflicted the drive previously can be fixed. Once again, cross-flashing is not a guaranteed solution, but it can work wonders in certain circumstances. I suspect that in your case, the latest version of the firmware available for the DW1620, which is B7W9, may help. As you did before (although it was unnecessary previously, since BQFlasher is only needed when cross-flashing, not flashing regular firmware), you would need to use BQFlasher to cross-flash your DVD8631 into a DW1620. Please be CAREFUL and make sure that you have checked and double-checked everything before you attempt a cross-flash. Flashing the wrong firmware on your drive will turn it into a doorstop. You have been warned.
Lastly, I definitely think you should buy some new DVDs (and if you can’t get out, ask Mom or Dad to get them). The media you are using is actually pretty rare, and to be honest, one thing you could do, depending on how many discs you have left, is to try selling them on eBay. There are a lot of people out there, many of whom frequent forums like CDfreaks, that actually collect old and rare media like that, and you might be able to make some money and use it to buy some new discs (that way, Mom and Dad can’t complain about spending their money). Just a thought.
Once again, welcome.