The next step that the technician should do to troubleshoot the issue is C. Swap the power supply if it is inoperable.

A power supply is a device that converts the alternating current (AC) from the wall outlet into direct current (DC) that the computer components can use. A power supply is essential for the computer to boot and function properly. A faulty or inadequate power supply can cause various issues, such as no power, no display, random shutdowns, or beeping sounds.

In this scenario, the technician is trying to fix a computer that fails to boot even when all the RAM is removed. RAM stands for Random Access Memory, and it is a type of memory that stores data and instructions for the processor to access and process. RAM is also essential for the computer to boot and function properly. A faulty or incompatible RAM can cause various issues, such as no boot, no display, blue screen, or beeping sounds.

One of the basic troubleshooting techniques for a computer that fails to boot is to remove all the RAM modules and try to boot with one module at a time in different slots. This can help to identify if the problem is caused by a bad RAM module or a bad RAM slot. If the computer still fails to boot even when all the RAM is removed, it means that the problem is not related to the RAM, but to another component.

The next step that the technician should do is to swap the power supply if it is inoperable. This means that the technician should test the power supply with a multimeter or a power supply tester, and replace it with a known good one if it is faulty or insufficient. This can help to determine if the problem is caused by a bad power supply or a bad motherboard.

The other options are not the next steps that the technician should do, because they are less likely or less effective. Inspecting the motherboard for swollen capacitors (option A) may be helpful if the problem is caused by a damaged or defective motherboard, but it requires opening the computer case and visually examining the motherboard components. Replacing the CMOS battery (option B) may be necessary if the problem is caused by a low or dead CMOS battery, but it usually affects only the BIOS settings and not the boot process. Checking to see if the HDD power connectors are well seated (option D) may be useful if the problem is caused by a loose or faulty HDD connection, but it usually affects only the data access and not the boot process.

For more information about troubleshooting power supply and boot issues, you can refer to the following web search results: [How to Troubleshoot a Computer That Won’t Turn On], [How to Test a Power Supply Using a Multimeter], [How to Fix a Computer That Shows No Sign of Power], [How to Troubleshoot Beep Codes].