Is the problem moving them ASAP or moving them with the least delay while in transit? If you have enough time to buy airplane tickets at a reasonable rate it can often be more cost effective to fly someone to pull the gear and fly with the boxes. I pulled and moved a rack full of servers in and out of colos quite a few times, flying out with new equipment and bringing the old equipment back, or flying out with empty boxes and packing the equipment in the right boxes (with the right foam inserts etc.) and bringing them back. You can save quite a bit by not having to pay "remote hands" at the other end to pull and pack the gear.
I believe that most airlines allow you 3 items of checked luggage up to 70 lbs at no additional charge. Extra checked items were ~$50 per box, and occasionally ~$50 extra if the box is overweight. I had a carry-on for my personal needs (clothes, laptop).
If you need a rental car, get an SUV and get one where the rear deck "folds down flat". The largest passenger SUVs (like a Lincoln or Ford) sometimes have a rear seat that sits on top of the rear deck and can NOT be removed, check this when making reservations as it's a big PITA to put boxes in and over this lump. I highly recommend a Durango instead.
Every time I shipped boxes instead of flew with them there were shipping delays. *Especially* when going thru international boundaries. When I took boxes with me thru customs as checked luggage, no delays.
If the computers you need to move are going to or from the west coast, I'm available if you want to hire someone to do this, if you can't spare a person to fly. Email off-list.