How do I find out, whether my drive is capable of burning DVDs or not?

Please send us the output of the following Terminal commands:

sudo aptitude update

sudo aptitude install hwinfo

hwinfo --cdrom ; dmesg | grep rw ; cdrecord -scanbus

system>admin>disc utility>there you should see your optical drive

Here is the output...

cyberix@eval:~$ hwinfo --cdrom ; dmesg | grep rw ; cdrecord -scanbus
31: SCSI 100.0: 10602 CD-ROM (DVD)
  [Created at block.247]
  Unique ID: KD9E.fViI5MnVCaE
  Parent ID: w7Y8.WveB18wNpNB
  SysFS ID: /class/block/sr0
  SysFS BusID: 1:0:0:0
  SysFS Device Link: /devices/pci0000:00/0000:00:1f.2/host1/target1:0:0/1:0:0:0
  Hardware Class: cdrom
  Model: "HL-DT-ST DVDRAM GSA-U20N"
  Vendor: "HL-DT-ST"
  Device: "DVDRAM GSA-U20N"
  Revision: "HX10"
  Driver: "ahci", "sr"
  Driver Modules: "ahci"
  Device File: /dev/sr0 (/dev/sg1)
  Device Files: /dev/sr0, /dev/block/11:0, /dev/scd0, /dev/disk/by-path/pci-0000:00:1f.2-scsi-1:0:0:0, /dev/cdrom, /dev/cdrw, /dev/dvd, /dev/dvdrw
  Device Number: block 11:0 (char 21:1)
  Features: DVD
  Drive status: no medium
  Config Status: cfg=new, avail=yes, need=no, active=unknown
  Attached to: #21 (SATA controller)
  Drive Speed: 24
[ 2.061113] sr0: scsi3-mmc drive: 24x/24x writer dvd-ram cd/rw xa/form2 cdda tray
scsibus1:
 1,0,0 100) 'HL-DT-ST' 'DVDRAM GSA-U20N ' 'HX10' Removable CD-ROM
 1,1,0 101) *
 1,2,0 102) *
 1,3,0 103) *
 1,4,0 104) *
 1,5,0 105) *
 1,6,0 106) *
 1,7,0 107) *

I see my disc at system>admin>disc utility, but selecting it doesn't reveal whether it can burn DVDs or not.

The Terminal output confirms you have a DVD rewriter. It can write to DVD's and CD's:

http://support.euro.dell.com/support/edocs/storage/P199472/en/intro.htm

http://www.ultradrives.com/product_info.php/products_id/1446