I have a emachines w3615 and it wont boot error message is pxe e61

that is a great post , and PXE is clear known well error.
This CMOS coin cell is dead.
now NVRAM forgot all setting, for BIOS
now from that act, PXE gets turned in BIOS and must not ever be.
PXE means remove LAN server boot, (thin net) for businesses.
never you.
the fix is 10 steps.
New coin cell battery
the reset bios like this. 9 simple steps clicks)
https://www.pcdied.com/cmos.html#Reset_only.

The error PXE-E61: Media test failure usually means the hard disk has failed or the hard disk needs re-seating or the disk controller is faulty. First - re-seat the hard disk and reboot the computer. If the computer does not boot up then reboot and go into the BIOS configuration to see if the BIOS detects the hard drive. If it doesn't detect the hard drive then it could be faulty.
Then the hard drive needs to be replaced in the computer/laptop, Windows installed and the computer or laptop's device drivers plus your programs etc. to get a functioning computer/laptop again.

check your boot order in your bios and make sure the hard drive is the first boot option.

The PXE error message suggests that your computer is trying to perform a network boot which is why it is saying there is a cable issue.
Check your BIOS settings and disable the option to boot from the Network, plus check that the computer is configured to boot from a valid internal hard disk drive. It is Ok to have a CD or USB device listed ahead of the hard drive in the Boot order as this is normal to allow booting from CD or DVD media or USB devices.
Check that internal hard disk is operational, that the cables to it are firmly connected at both ends (the drive and the motherboard).
If you still have a problem, then provide more information on what symptoms or error messages your are seeing.

The system is not finding any bootable media (Hard Drive) and is attempting to boot via the network card (PXE Boot) the error message is saying that there is not PXE network to boot from and it is exiting the process.
Generally, this is caused by a hard Drive failure. Reseat the drive and or drive connections and see if the system will find the hard drive.
Generally, a Hard drive failure

The PXE-E61 is the error code for No Network Bootable Device Found. Which means the computer cannot find your hard drive and is looking for a network drive to boot from. Either your internal hard drive has failed, or it is not seated or operating properly. Troubleshoot the hard drive, either it is dead or there is an interface problem between the drive and the motherboard or BIOS setting.

PXE means Pre-Boot Execution Environment. You see this message when the laptop trying to boot from a remote server using the network card. If you didn’t see the PXE-E61 message before, it means that the network card was listed after the hard drive in the boot order (you can set the order in BIOS) and the laptop booted directly from the hard drive. Now, when the hard drive has failed, the laptop cannot detect it and tries to boot from the next available device – the network card. Your laptop is not configured to boot from a remote server using the network card, that’s why you are getting PXE-E61 Media test failure error.

You have to replace the hard drive and reinstall the operating system?

You see this message when the laptop trying to boot from a remote server using the network card. If you didn’t see the PXE-E61 message before, it means that the network card was listed after the hard drive in the boot order (you can set the order in BIOS) and the laptop booted directly from the hard drive. Now, when the hard drive has failed, the laptop cannot detect it and tries to boot from the next available device – the network card. Your laptop is not configured to boot from a remote server using the network card, that’s why you are getting PXE-E61 Media test failure error. You have to replace the hard drive and reinstall the operating system.

Not always the Hard drive, boot into the bios setup utility and de-select network bootfrom the boot options. If it tries to network boot first you will always get that failure.