Hi

Can anyone recommend a silent, low-profile PCI-express, full HD card?

 cheers

 http://www.amd.com/us/products/desktop/graphics/ati-radeon-hd-5000/hd-5450-overview/Pages/hd-5450-overview.aspx

Just make sure you have enough room for the heatsink.

I'm an NVidia fan myself. eVGA makes some 9400 GT low-profile cards. They have a fan but will only turn on when needed. For HTPC usage this is infrequently. You can also get some GT220 in low-profile but I try to stick to eVGA discrete boards when possible.

I don't know how "high end" you are looking to go, but I've had good luck with the Saphire 4650 based card:

 http://www.newegg.com/Product/Product.aspx?Item=N82E16814102829

I have it in a Dell studio slim that is my HTPC and don't have any issues that I've notices over the past 6 months.