It's been so long since I've used PageMaker that I don't remember whether printing files with placed jpegs to a non-PostScript printer sends the jpeg data or the preview. Other image filetypes like eps would send the actual eps data to a PostScript printer, but only the preview (the portion of the image that displays in PM) to a non-PostScript printer like most inkjets. The solution is to print the PM file to a virtual printer to create a PostScript file, and use Distiller to change the PostScript into a PDF, which if done correctly, will produce a PDF with all of the image data that can be printed to a non-PostScript printer.
Whether your (presumably) newer computer with a newer operating system can print to a PostScript file or not I couldn't say. I've always used Macs, so I don't know how to do it in Windows (any flavor). Since you are new to PageMaker, may I suggest you check out InDesign. It is the successor to PageMaker, and works very similarly, only better. You can download a trial version to see if you like it. I think the trial version works for 30 days, then stops working until you enter a serial number (that you would get if you bought it).
At guess, you're using low-rez (i.e. screen rez) JPG images.
TIFF is preferred format for quality output.
Also, in PageMaker's print dialogue, click on the Options button and set the "Send Tif/Images" option to Normal and NOT to Optimized. The deceptively-named optimized option actually downsamples your image for faster draft printing and can significantly reduce the printed quality of your placed image.
Here's the knowledge that was accumulated in old AdobeForum PM section about importing images and common issues.
http://bigjohnd.org.uk/PM_FAQs/imported%20graphics.pdf (PDF, about 900kb - note that many of the links are now obsolete)