DC 17V from PC power supply?

neither, both -5 and -12 are typically capable of less than 1A (0.2A on a device at hand)

-5 has been discontinued in new PCs

If you need 17V and 4A you could try an aftermarket adjustable laptop power brick, It might be easier to find one at 18V or 16V though, but there are 17V ones out there.

Which I find all the time in the garbage. Or that time I needed a power supply for a Powerbook 1400, I opened up an inkjet printer I'd dragged home from the garbage, and it had the right voltage (those tend to have higher voltages than +12, but still decent current). The external power supplies have the advantage that they are already cased. The inkjet supplied a standalone power supply board, making it easy to extract, but not casing.

But, the problem is that applying voltage to a battery isn't a good thing, if the battery is some more recent kind, it needs a proper charger.

Michael