Incremental backup in postgresql
OK - if you can't dump + restore, and don't want to understand your system well enough to set up replication then you've got only one option left.

You will need to run identical setups at each end (version of PostgreSQL, 32/64-bit, compilation options, file paths etc).

Then, scp the entire data directory - including all the WAL files (pg_xlog) and all other sub-directories.

During a quiet period, halt your primary server and use rsync to bring your copy up-to-date with respect to the original. Then, start the copied server and off you go.

Whether you can do this in less than 4 hours, I don't know. It will depend on how efficient rsync really is, the latency between both systems, how many updates you have had etc.

It might be that running rsync before halting the primary server will make the real run go faster. Difficult to say.