Humming and noise is a fact of life with amplifying electric guitars (especially those with single-coil pickups).
A preamp will just make it all louder, and since your signal is already at line level, there's no point unless you want the coloration imparted by a mic pre. It certainly won't reduce the noise.
Try what Adam suggested. Also try turning around until you find the position where the noise is minimal. It could be that you are in a lousy place to record. My brother-in-law used to live on a hill about 1/2 mile away from a very powerful TV and radio tranmission tower. His guitars hummed and buzzed something awful, and there was really nothing he could do about it...
You can use a noise gate too, which, if set properly, will turn the volume off once the signal from your guitar drops below a certain threshold, so it won't be humming when you're not actually playing...
