I have a discman that will not read CD-Rs, only pressed CDs, when it's on battery power (same whether alk. or nimh). When it's running on a 4.5 volt AC adapter it wil sometimes read CD-Rs, maybe with several stops and restarts it will finally read the disc. But, on a hunch, I tried it with a 6volt adapter and it will read the CD-R every time.
What is the specified input voltage for your PCDP? I would not exceed that voltage if the longevity of the player is a concern. The player may have its own internal regulators so there may be some margin but they can be fried with excessive voltage.
Power supplies can be tricky. Some are "regulated" and others are "unregulated". "Regulated" power supplies provide the fixed specified voltage right up to the specified max current rating of the supply. "Unregulated" power supplies provide a varying output voltage depending upon the current draw -- as the needed current goes up, the output voltage drops.
The sticker on the bottom of the player calls for 4.5 volt. I've tried 3 different adapters, the original Sony, a generic 4.5 750ma and a Sony car DC 4.5 V adapter. I guess all 3 are unregulated since they don't specify otherwise.
I do think the player is messed up, since besides the CDR problem the headphone out sounds hideous on battery power and not nearly so bad on the 6V adapter. But I want to use this as a transportable because the line out is rather nice sounding. But I never take original CDs out of the house, only CDR copies.