I have been working on a remote stored file on one computer, but when I access it on another computer I get a big red "X" through a part of the file that has an image on it and it says in watermark that the "Link can not be found".

Why does it work on one computer but the same file doesn't work on the other computer?

Thanks!

I've had the same thing happen to me.

In my case I use a USB flash drive to keep my artwork on. When I use the flash drive at home the drive it is the "e:" drive, but when I use the drive at work it gets allocated as the "g:" drive. Inkscape saves the last file path used and attempts to use that. So when I use the computer at work Inkscape looks for the file on the e: drive and obviously it isn't there because that's not the flash drive on my work computer. Inkscape doesn't know that you're on a different computer, and that the file is still there just with a different path. From our human perspective the file is still where we last left it, but computers are more literal than we are. This is probably the same type of thing you're experiencing.

When you use an "external" image in an inkscape drawing, the image itself is not automatically embedded in the drawing, Inkscape only uses a link to the file on disk.
When you open the drawing on another computer, you need to have a copy of the image file as well.