If your noise changed, then either your equipment or environment changed.
Your connection could be considered either, depending on it's role. It could be adding noise itself, or it could have changed the voltage your pickups are operating at and increased their sensitivity. Messing with the volume control could help identify a line voltage issue. Your pickup switch will have a capacitor inline which determines the attack of your notes. I put in several capacitors on a rotary selector knob to choose my attack, but capacitors also function somewhat as line conditioners and the same solution may serve that purpose as well.
The first thing to check of course is whether it's even your guitar or any thing at all plugged into your amp, but if only your single pickup is problematic, you've figured that out already.
It could be line noise or picked right out of the air. If it only occurs with the singles, not the humbuckers, that leans toward radio noise.
Curing radio noise involves better shielding or removing sources of radio noise. Curing line noise can be as simple as placing a battery powered stomp-box with an op-amp isolator and phantom power in the effect chain next to your guitar. Try some different pedal effects and see if that helps.
Most likely your noise is AC wall hum which fluorescents, CRT monitors, wall worts, and several other appliances might produce. That would have a 60hz hum, somewhere between B and Bb. Any other frequency, and it's likely to be your audio gear itself.
Power conditioners exist for both wall hum and other frequencies, as do inline anti-noise devices dialed in to similar frequencies. You can also get battery blocks to plug your devices into instead of wall worts, which are essentially magnetic coils reaching through time and space to commune with your pick-up coils. The further away the better.
All wires are antennae, and all antennae have multiple ideal lengths to resonate with different wavelength signals. Simply laying power and audio cords out with different curves, stretches, or coil diameters may lose your noise.
Also make sure your appliances like refrigerators are properly grounded.
You don't have what option? ..Unplugging your laptop charger? You could get an external battery to replace that too, though that's rather desperate.
Presuming your noise is consistent, and since it seems you are recording with software, you should be able to find an anti-noise plug-in for your recording studio which simply uses your unplayed guitar noise as a reference recording to subtract from your input.