You might be able to run it over port 80 which is never blocked... The only problem with this is that you would probably have to connect your server directly to the modem... And not have a network or router.... Because once you introduce a router into the system... and there's more than one device on your local network... Then when people try to use your ip address:80 then the router won't know which computer to forward the Minecraft server traffic to...
I didn't really want to unplug my router and test out this theory... And i doubt you will either.... But i think it's possible with over port 80 with NO router, and the computer is directly connected to the modem.
Honestly, i would just go ahead & subscript to a cheap hosting plan... There are some really good hosts out there for under $12 a month...
Or just port forward your router & OS Firewall.