Okay, so I understand that this is probably a dead thread by now, but I really wanted to post this reply. First off, I'll just say that I haven't replied in so long because I've essentially had no internet at all since September. However, that did give me a few months to play around with Terragen a lot more, and I have to say... I'm quite pleased with it, now!
I ended up using Terragen 3 on the laptop rather than my brother's desktop computer because of noise, primarily, but portability (so that I can work on things while on the move, for instance.) However, what I ended up finding out is that, so long as I keep the laptop adequately ventilated, I can render things quite a bit better. I looked at the hardware to see if there was a distinct reason, and at first I was puzzled. Why? Well, this laptop's CPU only had one core! So then I looked at the RAM. Only 2GB! And then I saw the truly differentiating factor - the laptop uses Windows 64-bit, whereas my brother's desktop used Windows 32-bit. The laptop's also a little newer, so I think that the hardware's slightly more powerful, despite being a single-core CPU.
Now, I've been tinkering with the setting, practising and experimenting with all the little options for months, like I said. I've gotten pretty good at knowing what's what, and how to properly adjust the various settings to get the results that I want. I've even made quite a variety of scenes, even ones that I can now say that I'm actually quite proud of! Quite a few even look professionally done, I think (and I don't believe that to be boasting.) I just wish I had the money to get the commercial edition of Terragen 3 so that I could expand my capabilities, or even sell some prints of my renders. I've become that confident in my capabilities with this program (and I'm not the kind of person who ever has much confidence in himself regarding just about anything at all.)
I've found that, when I do raise settings that make a render very memory-intensive, I can just reduce the bucket sizes (128, 64, 32... for instance) while keeping the cache size the same as I would've for the original bucket size (256), and it will render even some of the most memory-exhausting renders, just with a little more time and effort. I've made incredibly complex and intricate renders that I would've never expected this laptop to make just by reducing bucket sizes to 32/32 and setting the memory cache to 800Mb. Having a single processor, this means that the single thread can invest 800Mb into a single rectangular spot that it is rendering at a time, while also being able to devote virtually 100% of the CPU - if I understand all this right. For a bucket size of only 32, this allows me to do even some of the most embellished renders on this very, very outdated system. I've tinkered with bucket sizes and memory caches, and it seems to come out this way every time: complex renders work best when I use small bucket sizes and an 800Mb cache, while simple to moderate renders work best with default, or slightly below default bucket sizes and the same 800MB cache (800Mb has just become my standard, as when I render, I turn off all other unnecessary programs to dedicate nearly the entirety of the RAM and CPU to the render.) With 2GB of RAM, and accounting for background processes that must keep running, I find that I frequently use 100% CPU and about 60-80% RAM for as long as 36 hours for the most complex renders and about a single hour for more simplistic renders.
Also, I think that the issue I was having before had to do with an attempt at using Depth of Field improperly, and having certain settings too high or too low. So, yes, I definitely agree that I was having memory issues and was just far too green to know what exactly was going on. When I turned off DoF and adjusted a few settings regarding memory and bucket sizes, all my problems were remedied! I haven't had that problem ever since. I've learned how to use DoF properly, now, but I don't especially favor it... I suppose I just tend to make images that have no need for DoF, but rather for broad, clear views with sharp focus throughout.
Again, thank you guys for all your help and sorry I just kind of fell out of the conversation. If it weren't for my internet troubles, I wouldn't have waited months to reply! I really appreciate everything you've all done for me, and how kind you've all been.