Hi Graham ®. Spare slot, black, 6in long. This is an ISA slot. I very much doubt that you'll find a Broadband modem to fit it. If the motherboard isn't one of those with a dodgy USB chip, then a USB modem is your best bet.
Hi Graham ®. The white 3 1/2in slots are pci. The Award BIOS 4.51 suggests to me that the motherboard has an Intel chipset and therefore the USB is also probably ok (is it a Pentium processor?). It was the VIA MVP3 chipset of that era that had the USB problem.
Hi again Graham ®. I used one of the Ebuyer USB cards on a motherboard with the VIA MVP3 chipset, and it sort of worked, with an ADSL modem but I think the problems were due to the motherboard not the card. I used the same card on a more modern motherboard and it worked fine with a printer and a card reader. Intel were much better at USB. You may even find a USB header on the motherboard. If you install and run Belarc Advisor click here or AIDA32 click here, you should be able to identify the make and model of the motherboard, and may be able to download the manual for it.