PicPick

(side note) You might be interested in portable applications. If so, https://www.portablefreeware.com/ is a good resource.

I found PicPick there.

I downloaded their portable version.

Unzipped it to a folder.

Ran it.

It captures the PrintScreen keypress by default. Which it did successfully.

I went into its options and turned on Auto-Save, and provided a folder, and changed the file naming scheme to a filename containing the date and time.

I took several full screen snapshots.

All this worked for me.

PicPick has editing features. I did not try them. But you could try it as an image editing program as well.

Resources for you:

PortableFreeware entry: https://www.portablefreeware.com/index.php?id=1496

PortableFreeware Forum Discussion: https://portablefreeware.com/forums/viewtopic.php?t=4596

PicPick website: https://picpick.app/en/

PicPick download page: https://picpick.app/en/download

PicPick portable download link: https://picpick.app/en/download/portable

PikPick direct link to portable file downloaded 02/17/2021: https://www.picpick.org/releases/5.1.4/picpick_portable.zip

(Note, without installing a program, you can always on bare-bones WXP do: )
 * Hit the PrintScreen key
 * Open MsPaint.exe
 * Paste (Ctrl-V)
 * File -> Save