From what you describe, the hardware should be fine.
Do you see the initial boot/bios screens? If you do it is likely the drivers. You will need to put the old card back in, uninstall all video drivers, then put your new card in.
If you aren't seeing the boot screens there could be another cause. (The installed drivers are not controlling the video output before Windows loads)
Your 650W power supply rules out under powering.
I would then suggest physically looking at the card and possibly (very carefully) check if the video card fan is spinning while the power is on. In addition if there are any LEDs on the card ensure they are lit up. This will ensure the issue is not a power problem.
If that appears to be okay, though you said there are no beeps, I would try disconnecting the power on the video card and see if you get any beeps. If you do not, you cannot count on your bios notifying you of the incorrectly connected video card.
A possibility is that this card uses fairly complex drivers, you should be able to install the driver without the card installed. You can always try using your old card, install the drivers for the new video card, then install the new card, but I can't guarantee this will work.
Let us know how it goes.