USB problem with macbook pro 13 (late 2011)

Hello,

I just recovered a macbook pro 13 (late 2011) 2.4GHz, Intel Core I5 running under 10.9.4.

One of the two USB ports on the left does not work at all.

The SD card is ok and 1 USB port is also OK, but the next one does not work.

I checked on some forums that a PRAM reset, or SMC reset would help. I tried both and nothing changed ..

When I put a device (key, hd or other) with a diode that illuminates the connection, nothing happens (whereas the first all goes well ..).

Anyone know it the problem and the means to solve it?

I have another problem (but less annoying), when I look on the battery icon (in the top bar) it is stated to check the battery ...

Is this battery problem may cause my USB problem?

Thank you for any advice ..