You should be able to find a Fujitsu Primergy TX100S3 for around 300. Then upgrade the memory and add a HDD or 2 and you would have a pretty good little host in a fairly small package.
I have the 2708 and it works just fine. The mounting brackets are multi directional so that you can easily mount the switch to a wall or under your desk. The 2808 is showing on Dells page as going for 99.
I have one and I use it for a pfsense box. I am using 11% of my memory and about 1 percent of my cpu. This is with heavy torrenting.
The box is quiet and cool, the switch that I have sitting on top of it puts out more heat than this little unit.
I almost betcha that I know what company you work for.
Another factor to consider is if this hotel is part of a national chain. Some hotels have been known for losing their flags for not sticking to the chains standards.
Another thing to keep in mind is what level of support are you...
BTW, not the wisest of things publishing your IP address out on the internet if you claim to have someone who works for the NSA living at your house. No telling who reads these forums and a bunch of info can be gathered by an IP address.
You might want to ditch the snapshot program as well. Programs to make your desktop prettier ususally come with unwanted presents. Also, you might want to disable utorrent when you are not downloading something.
It is going to take 4 to 5 hours to do a movie depending on the speed of your cpu, the faster your cpu the less time it will take to complete. It is a great program though and the quality is pretty good considering the compression that you get.
Just keep your firewall running on your pc, keep your virus definitions up to date on your system, and stay current on windows updates and you will be reasonably protected. Otherwise, if you are worried about becoming infected you would need to turn off your system when they are on your network...