Is it valid to use grape juice at Communion? Given that wine was used by Christ at the last supper, is it valid to use grape juice in the remembrance of the Lord's Table?
Yes, wine was most likely used by Jesus during the Last Supper, just as the cups in the Passover Feast are typically wine in today's observances.  Yet, there is not prescriptive command to use wine nor is there any prohibitive command against using grape juice.

If this were a significant issue, then it is reasonable to assume that the Bible would contain either a prohibitive or prescriptive reference somewhere.  After all, there are quite a few books, and Passover (which is what Jesus celebrated as the Last Supper) had been observed since Moses.

So, the conclusion is that it is not a significant issue and neither moral nor immoral to use wine or grape juice.  We do use the fruit of the vine, following the pattern in Passover celebrations, but the presence of fermentation is immaterial.  

The remembrance of the death, burial, and resurrection of Jesus Christ is supreme.

I might add that if you happen to live in a desert where no grapes can be grown, it would seem improper to assert that you could not celebrate communion since you would have neither grape juice nor wine.