I have tried deleting all my Starcraft files and redownloading the client, but this has not resolved the issue.
I am running Windows 7 (64bit). My computer hardware is the same as it was when I last played Starcraft II, and it worked OK then.
I am installing from the downloaded client as my CD drive does not work.
Any advice would be hugely appreciated.
Your thread has been randomly picked for an answer (mostly cause you asked nicely)
There are several thing you can try
1) Blame blizzard for removing the repair tool (seriously blizz, your launcher ain't gonna solve anything, let us be able to run the damned thing manually -> http://en.wikipedia.org/wiki/Thread_safety )
2) Defragment and error check your entire hard disk drive (right click each partition>properties>tools>defragment and error check is there). Note that error checking needs to be done before windows boots, so you need to schedule it.
3) you can try installing the game at a friend's computer and then copy paste it onto yours
4) take a look at this