Update: Sorry, left out a paragraph I meant to include.
If your image is not displaying, you should first check to make sure that the web site where your picture is hosted is correct. You can visit the URL with a web browser to make sure that you can see the picture. If you cannot, then you will need to find the correct location for the image.
Every picture you wish to display, must be hosted by a web site that allows remote loading to LiveJournal. Pictures hosted on your desktop are not actually on the internet, and cannot be seen by people who are not using your computer. Please note that many free web hosts do not allow remote loading, and the images will only display when you go to them directly or already have them cached in your browser. This may lead to you sometimes seeing your images and sometimes not.
Normally, your Internet Service Provider (ISP) will offer you some free web space as a part of your monthly account. You should check with them and find out if they allow remote loading to LiveJournal. If your ISP doesn't offer web space, or doesn't allow remote loading to LiveJournal, you will need to search for other sites and review their policies to determine if they allow remote loading to LiveJournal. In some cases, you may need to pay a small fee for the service.
LiveJournal cannot suggest image hosting services, as their policies can change with little to no notice.
Make sure that you either control the web space you are using, or have permission from the owner of the web space to use their images. Just because an image is on the Internet doesn't mean that it's available for use by anyone.
As long as you have properly inserted the code for your images to display, the actual displaying of the images will be entirely controlled by your image host. If your host has technically difficulties, does not allow remote loading by LiveJournal, or has a bandwidth quota that you exceed, you may find your images not displaying. You should contact the technical support for your image host for assistance on such matters.
To make sure you are using the correct code, see http://www.livejournal.com/support/faqbrowse.bml?faqid=6 for information on how to add a picture to your journal entries, or http://www.livejournal.com/support/faqbrowse.bml?faqid=97 for information on how to add a background image to your journal.