OK first I would be looking into the possibility of reflux - that can make babies scream in pain and also make sleeping up to ****. Also liking to be held upright all the time makes the pain ease for them. Please do not try Controlled crying because he already cries and doesn't sleep so it simply would not work, not to mention making a bad situation worse. Solids may help, but at this stage they are more likely to make the situation worse as well if the problem is a medical one. I would take him to your GP for some tests to rule out a medical cause and also take him to either a Chiro, osteo or a Bowen therapist as there could be an underlying musculo-skeletal issue that is causing him pain. Another thing I would highly suggest you get is a carrier or a wrap - either a Mei-tai or a hug-a-bub so that you can still hold him through the day and keep him upright but you can also keep going about your day as well. This may also help him get some much needed sleep too.

At this age they don't have the attention span for DVD's /TV so don't worry about that part of it. Not all babies like to be on the floor - either belly or back as they feel exposed and insecure kwim?

I really hope that you are able to find out what the issue is so you can start to enjoy your little boy and he can get some more sleep because I'm sure that is taking it's toll on you as well