Your car only turns right!
JavaScript (ES6) - 122 124 148 162 172 178 187 190 193 208 bytes
Many thanks to Optimizer and DocMax for helpful suggestions on how to improve this code:
F=a=&gt;(D=(x,y,d)=&gt;!D[i=[x,y,d]]&amp;&amp;(D[i]=1,x-=~d%2,y-=~-~d%2,x*y==49||!((x|y)&amp;8||a[y][x])&amp;&amp;(D(x,y,d)||D(x,y,~-d%4))),D(-1,0))

Returns true (truthy) for solvable and false (falsy) for unsolvable.
Works only in Firefox as of today becasue of JavaScript 1.7 features.
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