Manual Configuration of the internet connection speed

I have a home network consists of three computers, connected through a switch

One of them is connected to 100Mbps, while the other two computers are connected only if manually change the speed of the link / duplex mode to 10Mbps with a consequent slow connection. If I speed automatic link me rises to 100Mbps but does not connect, it say's connectivity is limited or nonexistent.

Does this problem may be my network card?

Maybe.
1 The network card is only 10, already has to be old conviction.
2 -cable not endure more of that speed.

Thanks for your answer but I do not think that is why.
The cable is I do not think compactable with another computer if you let me connect.