I don't have an open unit in front of me, so I'm guessing that this is a 1000uF, 6v electrolytic, and the year of manufacture is 1999. Electrolytics are easily damaged by heat, but before you remove it, test the circuit as follows:
1) Remove the CPU (you did remove the CPU before trying to remove Q16, didn't you?).
2) With the IO powered off, check the DC resistance between Vcore and GND with a multimeter. If it settles at less than about a few ohms, you've got a short and the cap is a good candidate for replacement.
3) Smaller values for this cap may also work, at the risk of high-frequency instability and higher ground bounce on Vcore. Use only SMT caps; the lead impedance on regular leaded caps is too high.
4) The FET Q16 is also easily destroyed, but more easily by static than by heat.