This seems likely to be your computer. I'm 99% sure that an Athlon that old lacks SSE2, which the Camera Raw engine uses if it can. Lacking SSE2 is likely to be a tremendous performance hit for all the floating point maths that is needed, also, if you don't have SSE2, you will likely have the "highlight bug" affecting some of your images (I understand that this is fixed in ACR 4.1 and should be fixed in Lightroom 1.1).
A 1GHz processor is pretty slow compared to what most of us are using anyway - and a machine of that age will be much more limited in memory bandwidth than a modern one, which means that Lightroom can't move data between the processor and the memory as fast as on a modern machine.
Is there any sign that the computer is thrashing the swap file (is your hard disk light stuck on)? A machine of that age will likely have older, slower hard disks, which won't help any. More RAM may help, but probably not that much - it's Photoshop that's the huge RAM hog rather than Lightroom.
Exporting to JPEG is a pretty time consuming operation - it's equivalent to opening a file in Photoshop via Camera Raw (remember that some of the adjustments available in Lightroom are much more processor intensive than those in the ACR 2.4 you'll be using with Photoshop CS), resampling if necessary, then saving as a JPEG. How long does it take you to do those operations with one file in Photoshop?
I think the hope of performance getting much better on your machine is very limited; Adobe have said, understandably, that the emphasis will be on improving performance for current and future machines. I suspect that there's very little they can do to optimise things for older hardware. In particular, it will benefit far more people optimising the code for SSE2 and SSE3 capable processors than to work on optimising the code for pre-SSE2 processors. Most compilers are pretty good at optimising code for the older processors already.
I think it's probably time to price up some new hardware. It can be a relatively modest machine - a fairly fast Core 2 Duo (Intel's price premium for the very fastest chips is rarely worthwhile), a competent motherboard, 2GB of RAM, a mid range PCI-E graphics card and a couple of modern SATA hard drives will likely give you a huge performance boost without breaking the bank. Each of these components has moved on significantly in performance from your machine (which must be around 4.5 years old and may be even older).
One thing you could look at is whether you feel able to exempt Lightroom from any on demand virus scanning on your machine. That may speed things up somewhat. Defragmenting your hard disk(s) may help too.
Do you really need all those (presumably large) JPEGs? I only create large JPEGs on the odd occasion that I need to send an original file out to be printed, or to someone else who is either going to work further on the image, or print it. If I'm printing myself, it doesn't get turned into a JPEG - I print from Lightroom instead.
That said, I still can't get over just how slow things are on your machine. On my relatively modest 3 year old laptop (Pentium M 1.6GHz, 1.5GB of RAM, 5400rpm hard disk), I just set a job going exporting full size images from my Canon 20D to JPEG. It's taking about 20-25 seconds per image.
There may be 1:1 previews for most of the images available to Lightroom (which Lightroom may well be able to use to speed things up), the processor has SSE2 and is around half as powerful again as your processor on general purpose processing (you can't make a direct clock speed comparison between AMD and Intel chips), also the machine isn't trashing its swap file (just as well, as that hard disk is terribly slow). It's a data point at least.
David