1) The Athlon 64's like to pull out of the socket when you try to pull off the heatsink. You need to give the heatsink a slight twist before removal.
It sounds like there was way too much thermal paste. Not a problem but messy. Clean it off and put fresh down. Arctic silver is best (any grade). Do not use the brown or white junk. It is junk.
2) If the pins on the processor did not get bent it is fine. If the pins did get bent they can VERY CAREFULLY be straightened. Remember to release the lever on the socket before trying to reinsert the processor.
3) If the CPU is dead the MB does not beep at power on. The beeps is the processor telling you something else is bad. The exact number and sequence tells you what is bad. The beeps vary with the kind of bios you have (Award, AMI, Phoenix, etc) so do a web search for beep codes for your processor type.
Here, your search results:
http://www.bioscentral.com/postcodes/amibios.htm
Once you get the CPU reinstalled unplug that slow fan just in case it is has a problem (it may not. Some MBs have case fan speed controls to reduce noise). Now boot and get the exact beep codes, number sequence, speed (fast or slow). You can look up what is wrong on the website above or post back here for additional help.
Assuming it was 1 long and 3 short that is a memory failure like Michael said. If you have the computer overclocked do a CMOS reset (instructions in the MB manual that you can download from Asrock if you lost it). COmputer must be unplugged from the wall and off for 5 minutes before doing the CMOS reset!!!! If it boots after a cmos reset quit overclocking.
RAM Checks
1) With power off, make sure your ram is seated in the sockets correctly.
2) Take out the ram stick in socket 2 and reboot. If it comes up the stick thats out is bad.
3) If it did not come up replace the stick in the first socket with the stick you removed. If it comes up the ram stick that is out is bad.
4) It is unlikely both sticks are bad but if neither works alone see if you can borrow a stick to try.
If you have 4 sticks the process gets more complicated but follows the same ]pattern try one stick at a time until you find a bad one.