Laptop Screen Destroyed - so how the heck do I transfer files?

Recently the screen of my laptop of 2 years (a Toshiba) decided to $&@! up in an unbelievably bad way, which obviously rendered it useless to me. So, I bought a new laptop (a cheap and cheerful Dell), with "Transfer MyPC" Software from Orlogix so that I could transfer my files from the defunct laptop to the new one. But on closer inspection I realized it says you must run the software on your OLD computer first before transferring the files from one laptop to the next, then select the appropriate cable when prompted. Now, maybe I'm being a little ignorant here, but seeing as I can't see anything on the Toshiba screen in the first place, let alone prompts, I'm not really sure how it will be possible to transfer anything. Is that me basically screwed, or is there something I can do without resorting to huge expenses?

 

Can you plug a monitor into the old laptop?

 

If the monitor has a VGA output, then you can plug a monitor into it. Some even have S-Video output as well.

 

If you cant connect monitor to the old laptop, remove HDD & put in an external enclosure.