I can well imagine your clients reaction if you suggest he or she buys a new PC..
Several things come to mind here.
You don't mention your clients system configuration at all and this is possibly where the problems lie.
Are they behind a network (and its security) or do they have direct outside access on a single PC to the web ?
Do they have a firewall (software or hardware or both) ?
Which browser are they using, what version is it and which version of Windows are they running ?
If, as you say, other people are able to view the site without any problems my first guess would be some form of security software is intercepting the images and preventing their display.
What is the file format you used for the site images and what naming convention is being used ?
The quickest and easiest way to check a site on alternative browsers is to install them on your development PC and test the site before and after it goes live in each one. Check PC Advisor cover disks for copies of some other browsers.
I keep Opera, NetScape, Mozilla and Internet Explorer on my main Windows development computers and I also routinely check my sites on one of my Apple Macs and in Konqueror on Linux, just to be sure the widest audience possible can view the site without issues.
I've not encountered a problem where alternative browsers were responsible for preventing images from displaying on a site unles the image was deemed some sort of advert. Some browsers and firewalls feature ad blocking and sometimes it can be a little too enthusiastic. That's why I asked about the naming convention you used for the images. Depending on how you name them they could be viewed as an ad and blocked by certain software applications.