Do I assume correctly that you can run Slackware as a liveCD; you just can't install it to hard drive?
If Slack doesn't run as liveCD, can you run a liveCD without problems, other than writing to hard drive?
If you have a liveCD you can run, try running it and run 'fdisk -l' to see if fdisk sees the disk and it's partitions (or lack of partitions). If fdisk cant't see the disk, you may have a communication failure (with the hard drive).
ide-cd: cmd 0x5a timed out
hdc: lost interrupt
This suggests to me that the failure to communicate with the hard drive occurs at the point modprobe tries to load the ide-cd module. That would happen if there is a drive failure. Drive failure in this case could be one of two things:
a) when you installed the new drive, you did not firmly seat the IDE cable. i.e., a bad connection.
b) the drive is bad out of the box.