Is it possible?
If it is, then how? and can i do it without the use of my diskette drive?

Bossen

Yes

Generally you boot from a floppy and install the new BIOS. Different motherboards work in different ways though.

Yes. Intel boards have a flash util that will run from inside Windows. You should check on the website of the motherboard manufacturer to see what options are available to you.

If there isn't one that runs under Windows, you will need to hook up a floppy drive and do it the old fashioned way.

Some newer boards have the flasing utility in SRAM/ROM but you'd still need to have the new bios on a removable medium that is mounted before the OS...