I have just set up ubuntu 18.04 and went through
an install of the HP deskjet 2652. Software seemed
to say everything is okay. I can print a text
file, no problems. If I try to print something
with graphpics though, like a jpg or pdf then
it responds that it is printing and shows on
the print Q, lpq, as printing but never prints.
also after this it will no longer print a text
file.

I tried printing a web page, went though all
the steps but never get a printed page.
Same with a pdf file, using evince to print,
no output.

Any clue as to what to look for, or why it has
problems with more complex files?

This is a long shot, but try opening one of the programs that is giving you print problems from the command line. Then try printing something; there might be some useful errors thrown to the terminal.

Also, for background, what procedure did you use install the printer (that is, did you use HPLIP)?

To see what's happening "under the hood", you'll need to examine the CUPS error_log file (/var/log/cups/error_log). Sometimes it helps to increase the CUPS logging verbosity for more detailed information related to the print jobs. That can be done with
Anyway, the general idea is to print something and examine the error_log. It's contains lengthy output, so not always easy to trawl through it. I sometimes delete the file (as root), restart CUPS and then send a print job so that there's only one job to examine. Anyway, if you want to share the output so that others can advise further, it's best to use https://pastebin.com/ and post the link to the output here.

BTW, I assume that you're using an HPLIP driver for this printer model? It may be that there's a missing/incompatible supporting library. You can use the HP diagnostic utilities to investigate that. Two such utilities are 'hp-check' and 'hp-doctor'. Run them from a terminal window...

That third-part site lists the the HPLIP driver for Linux anyway. It's version is as follows:

Date of release: Jan 28, 2019
File version: 3.19.1
File Name: hplip-3.19.1.run

Best just to download it from here.

Yep...loggrap is a spammer; all posts have links to spam driver sites. Already reported.

Oh, thanks - missed that.