Right. this is my third attempt to post here - posts get deleted because I've previously logged in or some such. So last try.
Thanks to all. I suspect that Mavericks doesn't work very well with only 4gb memory. However, this mac is upgradeable - the current one is not, and not worth buying for that reason. Sales of this one overlapped with the latest one and mine is both new and does have Mavericks installed. I bought it in Dec 14.
Activity monitor shows very little memory hogging, other than the kernel and chrome. Memory pressure shows green. I've not tried Safari as it didn't work well with Snow Leopard, but I will. CPU usage is small %, and the 500 hard drive has 380+ free space.
I hadn't thought of the Apple warranty but after wrestling with the support site for a while i've managed to send a pdf of the receipt, with the serial number. Given the obscurity of this procedure I'm not expecting anything much from this, though I hope to be wrong.