As we speak I'm using an older Blackberry Charger, but that wasn't your question...
It could be that the cables you're using are for dedicated data transfer. The HTC mUSB cable supplies both data and power, but there are plenty of "cheaper" cords which do one or the other. Do you have older mUSB wall chargers that don't connect to the computer (which is what I'm assuming you're doing)? Try one of those out and see if it charges. Sometimes, generic cables have issues with contact points, and that's where your issue might lie. Also, check the USB-A end (the bigger one) and see how many contacts it has. That often determines the function of the cord. Example 2 contact points instead of 4 = charge only.
I do know that back in the day, Motorola recessed some of their pins (or altogether removed one) to ensure that Motorola phones used Motorola chargers only. That would cause phones to act a little wonky when they were connected if it wasn't a Motorola. But this was back with mini usb, so it may not even be pertinent...
Voltage wise, however, it should be just fine. There is the universal 5V/700mA voltage, so it's highly unlikely that's the issue. My guess is the cables aren't very good, or your phone has suffered damage (doubtful)
