I had a similar problem a year or so ago, somehow the throttle body was stuck (even though I had cleaned all of that within the last year. Shop said on my car the TPS unit down there is part of the throttle body and was fried so they had to replace it. Worked fine after they did that and gave it back to me. It shouldn't be in limp mode at all if they fixed the correct problem. There is also a TPS at the pedal as some have mentioned...
2003 Jet Black 330i - Headers; Rogue Ikon Exhaust; 3.46 Diff; UUC SwayBarbarians; StrutBarbarian; Evo III SSK w/DSSR and Weighted Knob; UUC Lightweight Flywheel and Performance Organic Clutch; AFE Intake; MTechII Bumper; Dinan Stage II Software; 8000k HID Fogs, Predator Orion; M3 Lip Spoiler; ACS Roof Spoiler; Beyern Mesh 19" Wheels w/Hankook V12 Tires; LED smoked lights; Tri Stitch M3 Wheel; LED Interior Lighting; DICE