How much impact does hard drive cache have on IO performance

The short answer is yes. Your total hard drive latency is the [seek latency] + [rotation latency].

The 10K RPM drive will have a smaller rotational latency due to its faster spinning and will also be able to read data off of the drive faster. What the higher cache will do is for writes. A cache is similar to a buffer. When it reads data from the disk it will store recently accessed data and data within the near vicinity for quicker access. This is called temporal and spatial locality. The higher cache will be useful if your access pattern is such that you read the same file a lot or the data is stored near each other.

Wikipedia has a decent page on disk caches.

I had this exact problem on a (tower) server just like you explain, and it was easy:

smartctl will output the serial number of the drive

Vendors sometimes ship their own specific tools, like hdparm, that will do the same.

So output the serial of the bad drive, and then use a dentist's mirror and a flashlight to find the drive.

On a rackmount you'll usually have indicator lights like other people have said, but I bet the same would apply.