My ladder does show up correctly on the gel, so this couldn't be the problem. The DNA should be of high enough concentration, but I'm now running a control gel with higher concentration of only undigested plasmid to check whether I can detect DNA in the samples.
The other possibility is that you really don't have any DNA in the tube. How was the DNA prepared?
The DNA was prepared by miniprep, in the same way that I normally get yields of a few micrograms/ul. Nanodrop confirms this high concentration, but nothing visible on the gel.
Thanks for your suggestion, like I said above I'm now checking higher concentrations of uncut DNA to see whether I can detect the DNA on my gel.