Please HELP my entire yard has been taken over by dandilions and other horrible weeds!!!?

My yard was neglected for years before we moved here, we raked everywhere trying to get all the dead gr out. Because there was such a build up of dead gr there has been no time or room for new gr to ever grow in. There for my entire yard front and back have been taken over by weeds. They are so bad they have grown in height enormously. I don't know what to do my fence is broken and neighbours are complaining its spreading. I bought Scoots Path Clear remover and wilson wipe out weed remover, for the bigger ones. I have a dog and realize he must stay off the lawn and i am willing to make sure that happens in order not to harm him. We hardly have any gr and i just don't know what to do pulling them out by hand would literally take days! What should i use to get rid of this all or does anyone agree i would waste more money buying a bunch of stuff and i should just hire weed-man to come in???? Please help i can't bare to have a horrible lawn such as this one!