In general when people feel down, unmotivated, and utterly unmoved by any inspiration they tend to find some outlet of expression that proves in itself to be utterly useless.  Mindless entertainment, such as watching TV, indulging themselves with food or drink, or any number of distractions from the state they find themselves in. 

I fall into this trap from time to time as well.  There is really nothing wrong with relaxation, and in fact it serves a purpose of regeneration, but it can often be overdone, just look at the obesity problem for evidence to that fact. 

The only way I've ever been able to effectively deal with lack of motivation when I'm in a "down" state, is to proactively destroy it with emotion.  Positive emotions can be used to revive a state of mind that is dull, and uninspired. 

Of course, anyone could have told you that.  My goal, however, is to remind you how to collect positive emotions, and use them, as a sort of "catalyst" to spark motivation in whatever it is you want to do.

My technique is to first smile.  Randomly and occasionally I will smile for absolutely no reason.  As I do this I'm automatically giving my body a physical signal, which it reacts to by encouraging those feelings of joy. 
Then I will generally laugh.  Laughter is a powerful motivator.  Obviously I sometimes need some help in finding true laughter, but you'll notice that even a fake laugh can almost immediately lift your spirits.  We often contain in our brains snippets of quippy material that we hold in memory, and we might as well put them to use.  Another tool is to visualize, where possible, myself in a situation where everything is lavishly beautiful. 

The best visualizations tend to be things I'm naturally passionate about, this can be anything really from friends and family, to long term goals actualized.  Live in the visualization and "feel" it as though you are partaking in whatever expression it has to offer, and watch as your mood jumps up several notches. 

With positive emotions you can drive yourself towards any goal.  Give it a try and see how it works for you.