How to test an iPhone 3GS? (doesn't charge, display not working)

Hey guys, this is my first post.
I registered to this forum in order to have some help from Youi

So, I bought some iPhone 3GS in stock on eBay.

Two iPhones have the same problems:
-display NOT working (nothing appears on Display but the digitizer seems to be OK)
-when I attach them to the PC, it doesn't recognize them (anything happens, even if I attach them for 2/3 hours).

So what could be the problem? How can I test their motherboards without a display (if the motherboards are "dead" I won't buy a new display).

Thanks in advance

UPDATE.
I searhed on Google about the problem and I found a solution:
-attach the iPhone to the wall charger for about 2 hours (in order to charge a bit the battery)
-then move up/down the iPhone's mute button (the button on the left) and keep holding home and power button
-after all this, I connected to my PC and it recognized my iPhone.

BUT, it seems that the battery doesn't charge with the cable attached to the PC AND in 2 hours it recharged ONLY 22%.

Is it the battery in the end of its life

UPDATE 2.
I left the first iPhone connected to the PC but it seems that the battery rest at 22%

I tried to turn on the second iPhone with the same way BUT my PC don't recognize it.

When I connect the iPhone to my PC, it says "USB Device not recognized".

So, what could be the problem with these two iPhones?

Can someone help me? Thanks in advance.

Is there anyone who can help me?

What could be the problem for the iPhone 3GS that has "USB device not recognized" problem?