- The Sun radiates around 1400 W for a single square meter of the Earth.
- This decays quadratially with the distance.
- 1 light year is around 60million astronomical unit (=Earth-Sun distance).
- The nearest star is 4 ly away from us.
Thus, the solar radiation is $\frac{1400}{100000000^2}$ W from 1.5 light year distance.
You will get 0.000000000000014 W for every $m^2$ of solar panel.
It is nothing.
(Extension: it is about a Sun-sized star from 1.5 light year away. But the sky has a lot. Although they are far more away. Maybe their summed result could be even thousands times better, but I think it is still far from be enough.)
Problem #2: On Newton's second law, you can only drive the spaceship, if there is something what you can shot out from it. The solar power gives energy (quite few), but if you solve this problem somehow... for example, you use astronomical sized (i.e. million km big) solar panel foils... even in this case, you need to have some fuel.
Although I wouldn't say it a completely dead idea; with solar power it doesn't seem to meaningful, but there is a so-named Bussard ramjet:

The idea is to collect the interstellar gas with big electromagnetic fields, fuse them in fusion reactor, and shot them out with the produced energy.
Even this idea is in best case in the very far future:
- Currently, we can't fuse even deuterium-tritium mix (although it will be possible in around 20 years) (more exactly, we can fuse them long ago, but not enough efficiently to get more energy from it as we need to invest to maintain the device)
- With hydrogen is it currently totally unreachable (but seems possible)
- The interstellar gas has around 1 atom per cubic centimeter, it should be very strong, very big, very sophisticated field which can collect it into the drive of the spaceship.