Right odds on it's setup of either the amp or guitar
Unplug, find somewhere quiet and listen to the natural sound of the guitar. Listen for buzz and ringing coming from anywhere it shouldn't like bridge, nut and tuners. If there's a problem here, it'll never sound right no matter what the pickup is...
Check the action, too low will loose a bit of tone and sustain. Check neck relief. Tension of the truss rod can do strange things to tone if it's too tight Check the nut height. play every note on the neck with constant picking force, see if there's any dead spots on the neck. Neck's are never 100% dead spot free but if there's a bad problem you'll notice a lack of sustain and woolley sound.
If the guitar has a problem, it'll allways be there.....however, it's pretty rare to get a total lemon, I fitted some BKPs in a £100 tele copy, made from ply....and it blows away many solid tele's!!!
Has the Tonelab got a headphone out? If so do you have the same problem listening using headphones - swap leads over too, just in case.
How are you setting up your rig? Start simple - just work on headphones with the Tonelab, or plug direct into the Amp. No reverb or other effects. Start with tones at 12 o'clock, gain set clean, and the volume to taste. Play all over the neck, check for strange sounds.
Turn up the gain to get some crunch going. Try and listen to the notes in the chord, listen out for any strange sounds........a good time to run through your favorite classic riff is now....
Up the gain to lead levels, listen for those wierd buzzes. Do not lower the mids!!! If you lower the mids you risk the problems of a muddy bottom and shrill highs.......
You want a balanced tone. You can add bass, but keep the mids up, likewise add treble and presence (you'll need less at volume)
You can do th above with either your tonelab, or the Marshall. I'd start with the amp. Getting digital simulators to sound good into an amp is hard work..........be carefull of going over the top with gain and effects.
AVT amps are a bit aggressive - you could bug your favorite guitar shop and try a few different amps, especially valve ones!!
At this point you should have a decent sound. I've got all three of those pickups, I'm playing a Nailbomb now, in between words....really should be sorting out my next guitar lesson, but hey.....tone is tone....oh, and it is definatly not thin...