1. Log into telnet in your old host's servers, go the your public_html directory, and type in the following command:
tar -cpzf yourdomain.tar.gz *
2. Now login to SSH in your Tech Logic account and go to your public_html directory. Then type in the following command:
wget 123.45.67.89/yourdomain.tar.gz
where 123.45.67.89 is your old website's IP address
3. Wait for the transfer to finish. Then type:
tar -xzf yourdomain.tar.gz
This can save you A LOT of FTP time, specially if you have a large website