Set up user@corporatehost.com as a proxy:
ssh -o 'ProxyCommand ssh -p 2424 user@corporatehost.com nc %h %p' internalcorporatehost
This is best used through an alias in ~/.ssh/config, so you can simply type ssh ich:
Host ich
HostName internalcorporatehost
User user_name_on_internalcorporatehost
ProxyCommand ssh -p 2424 user@corporatehost.com nc %h %p
nc is the netcat command, which must be installed on the gateway machine. If it's not available, install any of the versions floating around (you only need basic functionality). You may need to indicate the full path to the nc binary (e.g. /home/oleg/bin/nc).
If your ssh client is Putty, this answer at Stack Overflow should help.