...Get a real toshiba or dell serial number it's best to find one on eBay.
Once you have a serial/tag call up the company and say this: "Hi, I have been an avid user of your laptops for years. I have been using your laptops for my business even! So last night, I left my (insert laptop here) on download some work files. In the morning, the laptop would not turn on whatsoever. I tried removing the battery, (bs your troubleshooting steps here.) POINT AND CASE: It doesn't work.
Now, they should say: "It seems you are in need of a mail-in replacement/repair."
Tell them: "I would love that but I can't since I work for the county and all of my work files are on there." (If you are doing this on Dell, they may ask you to take the drives out. Tell them that's a hasell and you can't do that...you know the drill. Act upset.) They will either cave and order the replacement, or transfer to a supervisor. If they say the bullshit "Unfortunately our policy does not allow...blah blah blah."
Tell them you want a supervisor. When you get him/her act upset and angry about it.
They should now create a replacement order for you. This is confirmed working with Toshiba. Note: Please change the excuse from "left it on last night."