Awesome first post!
Like you I have trouble getting rid of old equipment, even when their power consumption outweighs their computing power.
An option that might be insanely simple for this is to simply use PlayOn. PlayOn has a mobile portion for the server that allows you to access via SmartPhone/mobile devices away from home. They've had trouble from time to time on local media, but last I checked it was working.
A few things you'll need to consider:
1) Internet upload bandwidth from your house, do you have enough? Check speedtest.net
2) If any files need to be transcoded you'll want to ensure the PlayOn server is on a PC/server that is beefy enough to handle it. On the fly transcoding takes a lot of processing power.
3) Changing IPs, easily solved with dynamic DNS like dyndns.org or a comparable alternative.
PlayOn has a free trial, you could just download that quick and test it out.
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