Maximum PC

I just bought this new router: http://www.newegg.com/Product/Product.aspx?Item=N82E16833156249. I have it all setup except for a static IP on the lan. On my old router I had the router setup as 192.168.0.6 with a subnet mask of 255.255.255.248 and it worked great for my needs. On this router if I try to make a subnet any smaller than 255.255.255.0 it says the LAN ip specified is out of range. I would really like to get this setup because I really don't like using DHCP.

If you can only use a 255.255.255.0, then just use a 255.255.255.0. Using a /24 rather than a /29 has no impact on whether or not you can turn off DHCP and use static addresses.

I know but I would like to use a /29 so that I don't have tons of unused hosts.

Also on a side note I'm having a big problem with my network card I just bought for my moms computer. It is this card: http://www.newegg.com/Product/Product.aspx?Item=N82E16833166038. It connects just fine, and it goes between a good and very good signal strength. Yet it won't connect to the internet. I can't even ping the router most of the time. Out of 10 pings to my routers IP, 8 of them said request timed out, and 1 of them had a 50% return rate and another had a 75% return rate. Needless to say I have no idea why it is doing this. I did an ipconfig /all and all of the ips were setup correctly.

I know the wireless works too because I have surfed the internet on my laptop and it stayed at excellent the whole time

I'd say turn off the wireless and see if you can isolate the issue by connecting machines back one at a time.

Still the exact same outcome. The computer has sent about 450 packets and only received 18, so for some reason it isn't getting any packets back?

To be blunt, does it really matter? You already have the DHCP server disabled...... Lock down the wireless well, and a 'large' (253 spaces) address pool isn't that much of an issue.
There's also the possibility that the router's firmware just doesn't like (read: the engineers said "who's going to do this?) the /29 subnet. Only way to tell for sure: try it as a /24 subnet.

As to your other issue: I can think of three simple things that'll cause the massive lost-packets problem - faulty NIC (swap with known-good), faulty/damaged LAN cable (swap with known-good), or faulty LAN port on router (move cable to another (known-good) port.)
Far more likely that it's hardware, than it is Windows.

Well thanks for that, I guess I'll try to RMA it with newegg tomorrow and get it sent back.