This computer had been having intermittent issues for awhile (would just lock up for no apparent reason). Recently, it failed to boot and was issuing a Dell beep code: four beeps.
Turns out this is an indicator of faulty RAM. I removed the existing RAM sticks one at a time and turned on the computer. This allowed me to identify the bad RAM module (the computer won’t start when a faulty RAM module is installed).
I ordered new RAM to replace the faulty RAM.
Installed the new RAM today (4GB PC3-10600 DDR3 RAM) and the computer is working perfectly.