If your PC has USB ports that you can specify the BIOS to boot from, an alternative would be for you to download the SL ISO and UNetbootin
, create a bootable USB pen drive (in effect, a fast 'LiveDVD'), boot it and install from that.
Another alternative is to install from one partition to another: see the SL Wiki article HOWTO: Run Sabayon Without Burning The Image
or Install any Linux distro directly from hard disk without burning any DVD
Yet another approach to consider would be to use VirtualBox and use 'Install to Hard Drive' to create a permanent installation running on a virtual machine.
External DVDRW drives are cheap these days, so if your PC has a USB port then yet another alternative would be to buy one, burn a LiveDVD and install from that: HP DVD556S-H02 8x External USB Slimline DVDRW Lightscribe £35.17
, Liteon ETAU108-01 8x Slim Top-Load External DVDRW £29.99
, External USB 2.0 Slim DVD CD R/RW Drive Burner Writer £27.99