The method that worked for me [link|https://discussions.apple.com/thread/955927?answerId=5065355022#5065355022|was described by Saul123 on August 5, 2007|new_window=true]. I have previously tried every other solution I could find and nothing worked (i.e. putting device to DFU mode didn't work), the device was not being detected by PC or Mac. The trick described by Saul123 helped me to revive iPod Classic 5th Generation 60GB that's been sitting for 10+ years, I even didn't have to swap the battery.
In case the [link|https://discussions.apple.com/thread/955927?answerId=5065355022#5065355022|link to original post|new_window=true] stops working, here's what I did:
# I hooked up my iPod Classic 5th Generation 60GB to Apple 20W wall charger via Apple 30-pin cable.
# I pressed MENU+PLAY buttons simultaneously for ±10 sec until the Apple logo appeared on screen.
# I released MENU+PLAY buttons for split-second while Apple logo was still on screen.
# I kept repeating steps 2 & 3 in a loop for about 5-6 times.
# On the 3rd time I felt the HDD started spinning, but I kept repeating the 2&3 steps loop.
# I released all buttons after 5th-6th loop.
iPod Classic then displayed full-color black screen with a lot of colorful dots on black… and booted! It shows a battery charging indicator in the top right corner and all menus are working, music is playing. I have yet to see if it works without being connected to the wall charger. But it is already a big success I'm happy to report!