Smoke and oil inside my player!?

I have a rather new (4mths old) SONY Divx DVD-player. It has been exposed to a lot of (sand) dust, but has been working without any problems. Untill yesterday, when - while on stand by - it started shooting out smoke from where the power plug is connected to the set. Afterwards I noticed oil seeping from this same spot.

As there still was a rented disk inside, we had to take the risk and plug the player back in to get the disk out nicely. The player worked, with all the welcome texts etc. on the display screen. I've not tried playing disks yet.

I opened the player, and it looked fine inside - apart from some clear oil on the base and between some of the... thingies(!) inside. I dabbed the oil away with Q-tips.

What now? Shall I try playing disks?