Problems with connection on new PC

So I got new PC few weeks ago, had troubles installing windows but finally fixed that, however there is one issue that remained even though I got new windows 7 copy.

Whenever I boot PC it can't connect to network for some 5-10 minutes, it keeps trying and I get connection for something like 2 seconds before it says "network cable unplugged". When I finally get connection it kinda works fine, it's stable but I only get 10Mbps instead of 40Mbps which I should have. Upload and ping are fine.

I've tried updating drivers both automatically and manually from Realtek
however nothing has changed.

I'm really worried that the issue might be within network adapter. Unfortunately I somehow managed to lose warranty list so I can't get help from service. I don't know much about these things but would it be possible(if it really is the issue with network adapter) just to buy a new separate network card and use it while ignoring the old default one? Aside from this issue my PC is working fine.

Thanks in advance.

Try in Safe Mode with Networking too.
Also download and make bootable Linux Mint MATE DVD/USB, boot with it and see if there are any issues with network.
In device manager - go into adapter properties - advanced - check Speed & Duplex setting (default is Auto Negotiate), try setting to a suitable full duplex speed yourself.
Also check with another cable.