I had a similar problem and managed to sort it out majorly by the following steps;
1. Mains condition - Approx £20-30 in the UK, it must state that it filters EMI/RFI
http://www.ebay.co.uk/itm/Tacima-CS...084096?hash=item2cac592400:g:9qQAAOSwHJhXM4QG
(If your in the USA, there is something on ebay for less than $5 which seems to do the same thing)
http://www.ebay.com/itm/5-Outlet-Su...010574?hash=item338b83eb4e:g:MzoAAOxyYSdTEKb7
(Everything plugged into this that is part of your rig... AXE FX, Computer, Speakers, Cab, Power Amp, whatever is in your audio setup).
2. Moving AXE FX a bit further away from your computer (my computer and power were the primary sources of electromagnetic interference)
3. Sitting/Standing a little further away from your computer when playing (especially when using single coil pickups), combined with turning slightly to the side if necessary.
Shielding your control cavity/pickguard is also a good thing to try (not done so myself yet but plan on it). You can use aluminium foil or copper tape.
Making sure your cable is good, you might be able to wrap aluminium foil around your old cable to see if getting a quality shielded cable would make a difference.
Mains conditioner and moving AXE FX II further away from PC if possible are the most important (mine used to be aprox 1.5 ft away and on the ground next to it, now about 2 ft away but higher than my PC instead of on the same level). Best of luck, shouldn't be too much hassle to sort out if you do a few of those things, and might cost you less than $5 if you get that EMI/RFI filtering extension cord.
When I next built a computer I am tempted to stick a aluminium or steel side onto it, and computers really seem to spew out a hell of a lot of electromagnetic interference/radiation, which is not only a nightmare for audio recording, but probably pretty detrimental for human health.
