Yes the drive is visible in Explorer and at least CDs are readable in it (I don't have any DVDs that aren't blank with me to test).
Here's the stuff from the log. The drive in question is D:
I 13:53:21 ImgBurn Version 2.4.1.0 started!
I 13:53:21 Microsoft Windows XP Professional (5.1, Build 2600 : Service Pack 2)
I 13:53:21 Total Physical Memory: 785,840 KB - Available: 95,196 KB
I 13:53:22 Initialising SPTI...
I 13:53:22 Searching for SCSI / ATAPI devices...
E 13:53:24 CreateFile Failed! - Device: '\\.\CdRom1' (D:)
E 13:53:24 Reason: Access is denied.
E 13:53:27 CreateFile Failed! - Device: '\\.\CdRom2' (E:)
E 13:53:27 Reason: Access is denied.
W 13:53:27 Errors were encountered when trying to access 2 drives.
W 13:53:27 These drives will not be visible in the program.
E 13:53:27 You need Administrative privileges to use SPTI.
W 13:53:27 No devices detected!
Edit: Fixed a typo