Last night I kept reading a little more and learned that for a spaceship traveling almost at the speed of light, all the radiations that arrives to the spaceship would be so shifted to the extremes (X-rays, ultra-infra-red) of the spectrum that nothing from the outside would be visible from the inside.

Not that I really understand these things, but I find that a bit strange. Wouldn't this effect depend on direction? So radiation travelling in the same direction as the space-ship will be shifted past infra-red, and radiation travelling the other way past X-rays. But won't light perpendicular to the direction of travel still be observable?

A more interesting question:
How would we relativistically simulate a space-fighting game with all these time dilatations in a multiplayer game? All controls/the behavior of the spaceship would slow down compared to the outside scene? That is an interesting game design question....

See the indie RTS Achron. It's not a space-fighting game, but it involves time-travel. You're asking about how to design a multiplayer game in which the players can be in different temporal frames. This RTS deals with a game design problem that seems similar: how to design a multiplayer game that allows each player to travel back in time and affect the course of game events. It's a very interesting design they came up with.

Sorry to throw the thread off-topic, back to talking relativity BTW, an observer traveling at near the speed of light would be able to see almost nothing. "light perpendicular to the direction of travel", from the frame of reference of the traveler, would necessarily have to emanate from a source that was traveling at near the same speed in near the same direction (i.e. an object that appeared, to the traveler, to be almost at rest). Since this is unlikely, you would see almost nothing.

An alternative way to calculate this is from the traveler's reference frame. He will see the destination as nearing at speed of 0.5c, but the distance to the destination is not 10 light years to him. Rather distance contraction (just as time dilation) plays a role here. Lorentz contractions on distance say the distance is now (10light years)/(gamma), where gamma is 1/sqrt(1-v^2/c^2)=1.15. So d=8.65 and we get the time to traverse this distance is 17 years again.

I played with the idea of incorporating relativistic effects into a video game a while back and was unable to come up with anything particularly compelling. The simulation is non-trivial. At relativistic speeds it becomes necessary to not have information transmitted instantly - you must be careful that everything is "seen" after a speed-of-light delay (at least), which makes simulation considerably more complicated. This is necessary, for otherwise you break causality and let things "see" into their future. So it is necessary to keep track not only of the current state, but of previous states. For a suitably simplistic game, this might be practical. I am also interested in the possibilities for a puzzle game to be made where you combine relativity with something like wormholes to create time travel if properly moved. (One of Brian Greene's books has an interesting section on this possibility: take one end of a wormhole on a long, fast spaceship ride and now you have temporally (as well as spatially) separated the ends.)

I've thought about making a game or just a toy where Physics are modified so c is something like 100Km/h, and relativistic effects are taken into account. I don't understand relativity well enough to really know how to make it or what it would look like, and that's precisely why I think it would be an interesting teaching tool to help people gain an intuition for how a relativistic world works.