Final Cut Express dropping frames

Question

Okay, I've used Final Cut Express before, but mostly just to do stuff to already-existing files. Recently I've been trying to get some footage of me playing video games, so I just use a splitter to simultaneously put it on the TV and also hook it up to my Sony DCR-TRV120. Thus I can watch it on the TV (much easier than the camera's tiny screen!) while also recording it. Simple enough.
The next step is to hook up the camera to the computer and import it in Final Cut Express...except midway through importing it always pops up a notice that says frames were dropped and that halts the importing. So I went into the preferences and told it not to abort when it does that. So it successfully imports it. Then when I play through the clip the audio gets progressively out of sync as it goes on, which is pretty annoying.
If someone needs the system specs, it's a MacBook Pro with OS X 10.5.6, with (according to About This Mac) a Processor of "2.2 Ghz Intel Core 2 Duo", and Memory of "2 GB 667 Mhz DDR2 SDRAM".
The thing is, I have some trouble believing it's a problem of the computer being too slow or the camera being too old, because when I took the exact same tape and tried it on iMovie HD, it imported perfectly. The audio and video are in perfect sync.
Now someone could say that I could just use iMovie to do the importing, but I have two problems with that. First, iMovie HD isn't supported anymore and I thus would prefer to not rely on it, and secondly because Final Cut Express is supposed to be the better product and I find it frustrating that it won't handle importing (one of the most basic of things!) as well as iMovie does.
Any suggestions on what to do?

Answer 1

I'm capturing to the computer's hard drive, there isn't anything hooked up to the computer other than the camera (unless you count the power adapter), and there's about 40GB out of 111 GB available.
The problem is actually less the dropping of frames and more the audio desync. I tested it out with a different video and it gave me the message:
"The audio sample rate of one or more of your captured media files does not match the sample rate on your source tape. This may cause the video and audio of these media files to be out of sync. Make sure the audio sample rate of your capture preset matches the sample rate of your tape."
I've seen this message before (and there was audio de-sync when it showed up), though curiously this time the audio actually wasn't off at all.
The reason I find this so annoying is that, once again, iMovie HD will get all of this perfectly, and I'd expect Final Cut Express to be as good or even better...