You stated that you used the system for 3 years without problems...
Hopefully your system is the victim of improperly seated components RAM Processor I/O Cards
Please download the Dell Precision T5500 Service Manual for reference
Refer to the following pages of the Dell Precision T5500 Service Manual for specifics...
Page 10: Power / Diagnostic Light Codes
1- Off 2- Blink 3- Blink 4- Blink ACPI S0, hand off to BIOS control System on. BIOS not execution. This is the transition state to POST states.
Page 79: Before Working Inside Your Computer
Page 2: About Memory
Pay special attention to the section on Memory Population Rules Make sure you follow to the "T"
Page 52: Heat Sink and Processor
If you are game to try reseating the processor / processors (depending on your system's configuration) visit your local Best Buy (or similar) and purchase some Thermal Paste.
Page 76: Expansion Cards
Reseat any Riser / Expansion cards
Page 80: After Working Inside Your Computer
I'm confident you will get to the bottom of this!