This sounds like a rendering problem.
1 how are you printing to this printer? Check and make sure you're sending PostScript and that the printer expects PostScript. If the printer expects PCL you're going to have a problem.
2 how much RAM is installed on the printer? PostScript needs space to run, especially if you have graphics. The printer ships with, IIRC, 16MB. I
think that there's a single DIMM slot and that it will accept up to a 128MB DIMM. I don't know if you have to pull the 16 to put in a new DIMM; I doubt it, no-one's made 16MB RAM sticks in quite a while, so that 16 is probably hard-wired to the printer. I don't know what kind of DIMM you need; if it's SDRAM, the price for a 128 will likely be on the order of $40-60. Check Crucial, I've found that they're reliable RAM distributors. I'd max the RAM if I intended to print layouts with graphics.
3 what kind of files print, and what kind of files don't print? Are there fonts which are common to both types? Are there graphics elements common to both? Are there fonts which are different, or graphics elements which are different? Warning: low-end HPs with low RAM really, really, REALLY don't like fancy stuff, such as lots of starbursts or lots of blends or lots pictures at funny angles, or, worst of all, a combination of all three. They
will barf.
4 Quark will read all kinds of graphics formats. Unless you have a really, really, REALLY good reason, stick with EPSes, TIFFs or JPGs. Use grayscale for monochrome or spot color, and CYMK for full color. PNGs will usually work. Mostly. Especially grayscale PNGs. It's a bad idea to use BMPs, PICTs, or GIFs.