DVD drive not open tray

My Samsung DVD drive does not open the tray Is it possible to repair it without opening the drive fully? it only opens with a needle or wire and for it to close I need to touch the tray after pressing the button

It is usually the tray drive belt.
Open the tray & you will see two pulleys & a belt on them.
I have removed & replaced them from just the tray door open.
Get you some stainless steel wire & bend it with needle nose pliers.
A couple of small hooks.
Remove & replace the belt with these.

For temporary sometimes a cleaning with a cotton swab & alcohol helps.
Wait for it to dry before testing.

I find a paper clip good for door opening.