Do I need to remove the plastic cap from the socket on the motherboard before installing the processor?

Yes, the plastic cover on the LGA775 / LGA1366 socket must be removed before installing the processor in the socket.

This applies to:

Intel® Celeron® Processor Family Intel® Core™ i7 Processor Intel® Core™ i7 Processor Extreme Edition Intel® Core™2 Duo Desktop Processor Intel® Core™2 Extreme Processor Intel® Core™2 Quad Processor Intel® Pentium® 4 Processor Extreme Edition Intel® Pentium® 4 Processors Intel® Pentium® D Processor Intel® Pentium® Processor Extreme Edition Intel® Pentium® Processor for Desktop