128K is slow. But for most modern use, so is 5Mbps.
In this case, anything less than around 5 Mbps is too slow.
In order to transfer 20GB in say 16 hours, a connection speed of at least 3mbps is required:
((20*1024*1024*1024*8)/(16*60*60))=2,982,616bps
Of course, one could round up to say 10mbps to allow for other uses of the connection bandwidth and to consider variances.
It is safe to say, however, that none of this talk of slow internet really addresses their initial requirement. Assuming, of course, it's not setup for some stupid spam garbage like Allan mentioned.
The issue here is that the system doesn't have the required uptime. Why? Because the person sending the file won't leave the PC on. What reasons there are for that, It's unclear. One can only suppose the existence of some nefarious entity preventing that option, such as an overweight housecat who would smother the PC and cause it to overheat if it found it to be on.
Dropbox can be used in this way. Once a file is copied to the dropbox location, the client program will upload data as long as it is on, including partially uploading it. If the PC is shut down and restarted, Dropbox will continue the upload from where it left off. Once complete the file will be visible on other systems connecting to that Dropbox account and the web interface.