As it happens, I too am currently accessing the internet via a 'live CD' (actually, the OS is cached to RAM, so the whole thing is completely virtual, requiring neither CD nor HDD).
The reason for this is that 6 months ago I suffered a disaster which required a complete reformat and reinstallation of both Winders and Ubuntu. I decided that was going to be the last time I would have to go through such agony, and I came across
SystemRecueCD. This is a tiny Linux (Gentoo) system on a disk, which also contains a program called PartImage. This little gem can take a snapshot of a diskdrive or partition, compress it, and save it - you are saving a snapshot of your installed OS. Then, in the event of such a disaster, you restore the image and the OS is back to exactly how it was when the snapshot was taken, fully installed and configured. Has to be said it's not the most intuitive of programs to use, and some knowledge of Linux filesystems is needed, but it does the job.
I've decided to make an image every six months, and that's happening as I write, which is why I'm only here virtually ATM. While it's doing its thing, I thought I'd try and get this virtual OS connected to the internet. If you can read this I suppose I must have succeeded.
Now, Martin, I'm thinking that it may not be a BIOS problem that you have, but a Master Boot Record problem. The MBR is a very small partition hidden away right at the start of your boot drive. It tells the BIOS where to look for the OS that it boots into. If you dual boot, then it points to where GRUB is kept (the little program that gives you the choice of which OS you want to use). If the MBR becomes corrupt, or GRUB gets messed up, the computer simply doesn't know where to look for an OS. This is the sort of thing that can happen if an update goes wrong.
But there are a couple more 'live CDs' that may help:
Super Grub Disk and
GAG Graphical Boot Manager. You will need to find a way to download and burn them to disk, but they may be able to restore your MBR (for Windows or Linux), or at least give you a way of finding the OS again.
If it turns out that you have to reinstall Ubuntu from scratch, then it might be a good idea to consider dividing you HDD into partitions, and keep at least your /home directory in a separate partition. By doing this, it should be possible to reinstall any Linux flavour without overwritting all your important data.