My Thinkpad T410 is loaded with Debian Jessie (usb thumbdrive).
/dev/sr0 exists, but mount reports "mount: special device dev=/dev/sr0 does not exist". The tray randomly tries to open and occasionly succeeds.
The bios has no information on the drive.

I normally use thumbdrives for data, but the repeated attempts to open are getting annoying.

Any suggestions?

Buy a New DVDRW. I went through this already on my DVDROM drive on My free Dell 755 server tower from city hall. Same symptoms as you describe. I found a used DVDRW on ebay for $2.49 olus shipping and all is well with it now. Watched movies, burned a music cd and a movie dvd.

You can do these commands to poke around. Just to learn something.

hit enter

look for sr0. But it says it is not there. But you can look anyways.

Make sure bios sees it and it is enabled also. My Dell has a on/off in bios for sata 0,1,2,3,4 bays to enable or not and will nag me at boot if it does not see the drive enabled.
Because the drive is bad. Not sure of IBM bios. My newest IBM is a E50 low profile desktop machine.

Another command to play with is

And

Edit: If I am way off base here. Because it works in Windows or whatever.

Should open it. But I am going by your statement that bios has no info on your drive which I find troubling.

Following the suggestions above I rebooted and checked the bios.
There is no mention of a CD or DVD in the bios.

/dev/sr0 does exist.

dmesg | grep -i cd-rom, gives these lines (plus some others)
[ 2.162329] scsi 1:0:0:0: CD-ROM HL-DT-ST DVDRAM GU10N MX05 PQ: 0 ANSI: 5
[ 10.968093] cdrom: Uniform CD-ROM driver Revision: 3.20
[ 10.989705] sr 1:0:0:0: Attached scsi CD-ROM sr0

more /proc/sys/dev/cdrom/info gives this info:
drive name: sr0
drive speed: 24
drive # of slots: 1
Can close tray: 1
Can open tray: 1
Can lock tray: 1
Can change speed: 1
Can select disk: 0
Can read multisession: 1
Can read MCN: 1
Reports media changed: 1
Can play audio: 1
Can write CD-R: 1
Can write CD-RW: 1
Can read DVD: 1
Can write DVD-R: 1
Can write DVD-RAM: 1
Can read MRW: 1
Can write MRW: 1
Can write RAM: 1

eject will open the tray just once after a reboot then never again.

mount -t iso9660 /dev/sr0 /mnt/cdrom gives the following:
mount: /dev/sr0 is write-protected, mounting read-only
mount: no medium found on /dev/sr0
and faild to mount a commercialy burned dvd.

Is this enough information to help diagnose the problem?

Try another live cd of another linux version other than what you are running.

MX14 is one that is good for seeing if this problem persists across distros and is a hardware problem then.

It fits on a cd and is Debian stable based and runs live. Go with the 32 bit version.
I am not sure why your cd eject command works just once after a reboot. To see if it is a permission issue.