Windows 7 - Unable to connect through router after W7 x86 install

Hello, new to the forums, stumbled here after trying to google up a solution to my recent network problems.

I've recently made a clean install of Windows 7 Home Premium 64-bit on my PC, and now I can't access my internet connection through my router. I'm currently connected directly through the broadband modem. I've tried connecting through wifi to the router with several other laptops (running different Windows- and Mac-OS' but all 32-bit) without any problems accessing the internet. Then I tried another laptop with 64-bit OS which didn't work, so I've narrowed down the problem to some conflict with the router due to 64-bit OS.

The router/modem is D-Link DIR655/Cisco 2100. Windows 7 is updated. Using ESET Smart Security 4 (v. 4.2.71.2) firewall and antivirus.

Guessing I have to change some settings in my router, but I don't know where to start, since I'm no network technician. Any suggestions on what might cause the problem?
Additional info will be provided if neccesary.

To clarify, I want to be able to connect to the internet through my router, right now neither cable nor wifi works. I can find the home network and other devices on it, but I can't access the internet.

You have two x64 computers that can't connect. Do both of them run ESET? If so, uninstall (do not disable) ESET and reboot to see if that's causing the problem

I'm pretty sure it's not ESET causing the problem, I actually had this problem even before installing it. The other laptop running 64-bit OS is not mine and is running Symantec antivirus.
My guess is still some conflict with the router.
EDIT: Thank you for the relatively quick answer though.

EDIT2:
Some additional info.
I've used dynamic IP-settings for all computers on the network without problems up until now.

An additional practical problem in trying to solve this is of course the fact that I can't access the router settings and still have access to the internet and check these forums at the same time...

1- I don't think x64 OS is the problem. Maybe you don't have a compatible "Network Driver". Check your "Network Adapters" in "Device Manager", is there a yellow triangle beside it?
2- Have you tried "Troubleshoot problems" in "network and sharing center"?
Mak

I'm using my built-in network card (on the motherboard) now with cable directly to the modem, and it obviously works, though when I connect through the router, I can't get it to work... Will look for the latest drivers for my wireless card (PCI, not USB-stick) now, but I don't think it will change anything. I'm getting the yellow triangle regardless of card when I connect through the router, I've tried to troubleshoot with no luck. It says I might have to input additional login information even though I'm successfully connected to the network (when on wireless), and since I use dynamic IP-settings from my ISP, I don't have any other login or dial-up information.

Just checked my drivers for both cards and they seem to be up to date. I'm still placing my bets on that it's the router causing this problem, since no computer running 64-bit OS have worked so far (though I've only tried with 2) when connected through the router.

These are my cards:
TL-WN951N PCI Card
RTL8169/8110 (built in)

Good news everyone, I got it to work! It actually turned out to be some regular IP and DNS hassle that I thought I had gone through... double-checked every setting on the other laptops again and found out they actually had specific DNS-settings that I must have mis-read the first time I tried.

I'm very glad for all the answers anyway, and I'm sorry for making an un-neccesarily long thread about this when it turned out to be so simple.