As I work in the computer field... Just replace the boards... but the Ham Radio Operator in me says, fix it...
I suggest a good soldering iron... Personally I use a Weller soldering station, temperature is variable, many different tips... Even a cheap 25W (dont get thoes junk dollar store units!) iron should be more than acceptable for the task. Stay far away form the dreaded solder gun... they are too big and too hot for what you need to do.
Get a solder sucker or even better some soldering braid.
Make sure to replace the caps with the same voltage rating and same value... the voltage rating could be higher with out problems, but dont change the actual value of the cap... if it is a 100uF cap, dont put a 110uf or a 90uf cap in there.. replace it with the same.
The voltages across the caps shouldn't be too bad... 5 to 12 Volts.. but I would still suggest discharging them through a 100 ohm 1W resistor, just for safety sakes.
Find out if the board is RHOS... because you may need to get lead free solder... but personally, I would use good old 60/40 or 63/37 Lead / Tin solder....
Use Google, and you will discover many soldering tutorials... check out some desoldering tutorials as well... you are going to need to remove the old caps.
Go take a visit to your local electronics shop... they may be able to help you get some of the tools you may need to start your project....
I hope this gets you off to a good start.
Let us know how this turns out!