Python distributed machine learning
This shouldn't be terribly complicated.

Big picture

Assuming you have Linux on your server: SSH to your server from your work laptop, train the network, receive results (the trained network).

Details

Train the network

If you want to stick with Python, there are two basic options that I am familiar with. 

The first is PyBrain, a library built specifically for training neural nets. The syntax is fairly straightforward. The dataset structure is a bit unusual (especially if you are used to just using numpy arrays in scikit-learn), but otherwise, it works rather well. However, it doesn't support GPUs AFAIK, and I don't know how optimized/fast it is.

The second is Google's Tensor Flow. A bit of a heavy-weight if you just want to run vanilla neural nets, but the syntax is also pretty easy to get around (although very different from PyBrain). It's also probably faster than anything else you could find in Python. It also supports GPU training.

Get the results back

This depends on the library you choose (or it could be definitely up to you write your own implementation). But both libraries mentioned above will let you return the trained weights, which you can save as csv files and download upon training. Or you could pickle them and get back that way. Also, Tensor Flow has this Tensor Board functionality which should let you visualize the training and the network structure, but I haven't tried it yet, so can't help on that front.