Does the same occur when pinging the router?

I ask because you should NEVER lose a ping reply on an internal network. At this point, I believe your network cable or card on that system is suspect. Might you have a spare of both that could be tried? One at a time of course for testing.....

Early this morning i tried some things i found on other topics and here are the results:

C:\Users\Nektarios>ping Google

Pinging Google [74.125.39.104] with 32 bytes of data:
Reply from 74.125.39.104: bytes=32 time=43ms TTL=242
Request timed out.
Reply from 192.168.0.5: Destination host unreachable.
Reply from 74.125.39.104: bytes=32 time=117ms TTL=242

Ping statistics for 74.125.39.104:
Packets: Sent = 4, Received = 3, Lost = 1 (25% loss),
Approximate round trip times in milli-seconds:
Minimum = 43ms, Maximum = 117ms, Average = 80ms

C:\Users\Nektarios>ping 74.125.53.99

Pinging 74.125.53.99 with 32 bytes of data:
Reply from 74.125.53.99: bytes=32 time=202ms TTL=45
Request timed out.
Reply from 192.168.0.5: Destination host unreachable.
Reply from 192.168.0.5: Destination host unreachable.

Ping statistics for 74.125.53.99:
Packets: Sent = 4, Received = 3, Lost = 1 (25% loss),
Approximate round trip times in milli-seconds:
Minimum = 202ms, Maximum = 202ms, Average = 202ms

As far as the cable is concerned,it is only 1 day old.I changed 2 of them in the thought that maybe there is something wrong with them.As far as the ethernet controller is concerned,in the device manager it says that it's working properly......

Yes, the ethernet controller is working properly - some of the time....

Perhaps another port on the router? I still believe that your network is iffy.

I have another computer in my room and i've been moving the same cable from one computer to the other while the other side of the cable is in the same port.One computer connects to internet normally while the other not.

I wanted to ask you,if you know of course,if there was something wrong with my network adapter,wouldn't it appear at the device manager with a yellow triangle underneath??or at least wouldn't the device manager indicate that there is something wrong with the hardware??

A failing network card isn't always failing - you've seen partially successful pings. Device Manager works similarly. The card is mostly working, so Device Manager reports that it is working.

You might try updating the problem system's network card driver - download on one system and move to the problem system with a USB drive.

So you have the opinion that i don't have any hardware problem?
I'm mostly concerned because my notebook is 5 months old and the appearing of such problems is very irritating!!!!

I have all new drivers already installed!!What else is there for me to do?

No, I believe that the network card in your system is questionable. If the wired & wifi are built into the motherboard, you might want to contact the manufacturer and request a motherboard replacement.