If you old board is an Asus P3V4X, it is a slot 1 board.
Your CPU is either a slot 1 or a S370 on a slotkit. Remove the CPU like you would remove an old Atari cartridge (pull straight out -- there may be side retention clips you have to undo first).
If it is a slot 1 CPU, the heatsink will generally be attached to the PCB (printed circuit board) with some sort of clip in the back. it will usually be the same length as the PCB also.
Under the HS/fan, the CPU core will be attached directly to the PCB.
If it is a s370 chip on slotkit, the heatsink/fan will be cliped on the socket on the slotkit by 2 little tabs. There will also be jumper pins visible & you will be able to see the lever to release the cpu from the socket.
S370 has generally replaced the Slot one (cheaper to manufacture). The slot 1 interface is a holdover from the Pentiun II and the Pentium III Katami's (the L2 Cache was off-die & needed to be mounted on the PCB).
Very few new motherboards are made with slot 1 now. I think there is only 1 i815 board & just a hadfull of VIA boards left.
You probably are best off selling the P3V4X and the PIII 800 as a combo & buying a new CPU. You can pick up another 800 for @ $135 new, or a 933 for @ $160 new. Look at pricewatch.com for prices.