I'd say it's definitely the first thing to try - that driver chip is clearly dead! Looks from your photos like they are socketed though, so no soldering required. Just remove the old one and replace like-for-like, being careful not to bend any of the pins.

Also, check to see if the chip needs to be electrically isolated from the heatsink. Some do, some don't - take your lead from what is currently there, and if the back of the chip is metal. If it needs to be isolated, then there will be evidence of an insulating pad or washer used between the chip and the heatsink, and then you need to take a lot of care when you fit it all together, testing it for isolation with a meter. But maybe it is just bolted together. Looks like there is at least some heatsink compound used, but what lurks in between is not visible in your photos. Try and salvage as much of that as you can for the new chip - ideally you'd buy a small tube off eBay and smear it on to help conduct heat from the new chip.

Hope that helps!
Graeme