Since it hasn't been mentioned yet... Yes a failing drive will significantly slow down a computer. Drives are built to be fault-tolerant, so if it reads a block of data and that doesn't match the block's checksum, the drive will attempt to re-read the same data until it gets what it believes is correct data, or until it gives up and sends a failure to the computer.

So now imagine your drive is in a state where nearly every block is having trouble being read, so it re-reads each block several times, adding a significant amount of time to every operation. A scan of the drive may indicate everything is working correctly if the drive does eventually return valid information, but the drive itself is having to work very hard to get this data.

One thing you might try to check for internal errors is running a read/write test of the drive, and recording the speed these operations were performed at. If that number is close to the parameters of the drive (you can check with the manufacturer or online reviews to find real-world drive speeds) then the drive is probably ok. However if the test is running a lot slower than the expected speeds, it's a good bet that your drive is failing and you will want to back up the data as soon as possible.