You most likely have a blown final stage resistor. Fairly common failure on the E39
Bring it in to BMW Excluservice we can diagnose it fairly quickly and provide an estimate for replacement at that time.
Kind regards,
Stephane Grabina
BMW Excluservice
Rockville, MD 20852
www.bmwexcluservice.com
RepairPal Certified shops can diagnose and repair your 2001 BMW 540i. They provide transparent pricing with a minimum 12-month or 12,000-mile warranty on repairs and services.
Thank You