In all fairness, if it was a case of fighting on the ground only (no orbital stuff) we would win.
Which is why it's unfortunate that the Imperium would be coming from orbit.
the Imperial guard wouldn't be to happy when they see that our tanks (Challenger mk.2, Abrams m1a1 and the leopard II for example) can hit their tanks from outside their own range, are less of a target due to their smaller build and have stronger armour.
What do they care? They have more tanks than we have people. And really why are they deploying so far away from us? Drop it on their heads I say.
The guard would win battle due to massive numbers, but they would take some pretty damn heavy casualties due to the weapons we use combined with out tactics. And seeings that our planes would easily beat the imperial flyer, we would own the skies, so with the support of planes and helicopters ground battles might actually swing our way.
Again, what do they care? The guard would be willing to blanket this world with their corpses if that was what it would take. They are perfectly willing to take these kinds of casualties. We are not. As soon as casualty reports start reaching civilians (which they will) you can expect massive backlash and a crumbling political will. They can and will sustain damages that we will and can not.
As far as space marines go, If a lasgun can has been seen to penetrate a suit of power armour, a normal 5.56mm round might strungle, but any of the bigger calibre ammunition wound probably get through, so 12.7/ .50 cal, 40mm grenades, 20mm & 30mm cannon etc. would probably do the damage. Besides, we have neutron bombs specifically designed to kill the people inside the armour.
Lasguns cannot penetrate power armour. Boltguns cannot penetrate power armour. Nothing shy of a hellgun (that word is better) can penetrate power armour. Guardsmen can occasionally kill marines by hitting them in the joints enough, unfortunately we don't have the numbers to just keep shooting at them while they butcher us.
The elite troops we have would be better than the elite troops that the guard have, sostrikes from them would be pretty effective against any groud based targets that the imperials would have, that combined with our arial support, naval capabilities and extreme long range smart weapons their supply routes and command structure wouldn't last to long once it has been located.
Why do you assume our special forces are better? No offense but how many of them have been raised from birth to kill? My money's on not very many. The Imperium breeds psyco-killers and super humans. People living on Catachan, Kreig or Cadia would all be superior (physically) to modern-humans. Thousands of years of selective breeding will do that.
Tactically we may be better but reading some BL stuff (Gaunt's Ghosts in particular) I get the impression that tactics aren't always that simple in 40k. Not to mention the fact that they have more tactical options than us, including another theater of war (orbit) that we can't even enter.
And as far as shooting nukes into orbit goes, good luck with that. We do not have the capability to launch nukes beyond our atmosphere. We do not even have the capability to go to the moon anymore. All the Imperium has to do is sit out there and occasionally shoot at us. Plus, I'm pretty certain that nukes are the standard in ship-to-ship combat in 40k (not certain on this) and so void-shields are perfectly capable of holding off at least a few. And if nukes aren't the standard than that means there less effective, because it means the Imperium rejected them as a weapon.
In conclusion. We'd be pooched. We wouldn't stand a chance.