Re: 35mm > HDCAM > FCP ?

First of all, possible and reasonable are two different things. I have mastered several feature length projects in Final Cut a dual 800 G4 (in the now distant past of course). I wouldn't pretend to bother with that today. If you have the time and patience you can use the system you have. I would though take it to at least 2 gigs RAM. The laptop is going to be a faster machine. Media storage is your biggest consideration with either set up.

Second. HDCam and HDCam SR are two completely different formats. One does not imply the other. If they have HDCam, then that is what it is. Get the transfer done at 23.976 frames per second. Apple likes to call this either 23.98 or 24 but it really has to be 23.976. There is a real 24 (which is true film rate) but that is a pain to work with, especially if the intended destination is video.

Don't even pretend you will be adding useful external HD monitoring to an old tower or a laptop on a no budget process. I would suggest a second computer monitor to give yourself some room.

ProRes is the most reasonable mix of quality and file size. It may be a little processor intensive on a G5. I've worked with it on a dual 2.0 G5 but can't speak for the 1.8. ProRes is a 10 bit format. Unless you have days upon days for rendering (for color correction, image scaling/cropping, titles, whatnot) you will be processing at 8 bit. A much more reasonable (but lower quality codec) is DVCProHD. The laptop should be faster, but with still only two processors, not by much.

Your new transfer will have new timecode. 23/24 frame rates have no drop frame timecode. You will be eye matching the new cut. Even if the transfer starts at the same number, it will drift from your offline as time goes on.

Buying/building a new system for a no budget job is not a reasonable consideration. If you want a better computer or or more complete system, look for a facility that will rent a suite to you. If that is still too expensive, at least then your client knows the value of what you can't offer since they wont pay for it.