Wow, so many responses! Thanks everyone.
@calico: Okay then. Well, that's good to know, and you're right - RAM doesn't cost that much. I've actually been considering building a new PC from scratch, but I've been putting it off because I don't really want to spend the money. If I'm going to need more RAM, though, I may as well finish the job... hmmm, we'll see.
@Mohawk20; PorcupineFloyd; Zylot: Thanks for the advice, guys. The crop render idea makes sense; I have a bad feeling I'm going to be using it quite alot!
@old_blaggard: That's very good to know! Thanks very much for confirming for me.
@plugsnpixels: Thanks for the example. And thanks for the info regarding Vue - it's good to know what I currently have renders faster, but it doesn't do me much good if it won't even start rendering my images. I probably should have mentioned that I've tried the same scenes on a dual-core 2.2Ghz laptop running Windows Vista, with 2GB RAM, and it still won't even start rendering.
Thanks again everybody for your advice - that makes my job alot easier! Hopefully I'll have something worth contributing one day.
Kind regards,

~Shashin