To eliminate some common issues here, try removing all RAM sticks from the laptop as well as the hard drive and the battery (run only on AC power via AC adapter). Power on your laptop again *with or without the case on doesn't matter*, and see what happens. Can you get into your BIOS (also called Setup) screen in this configuration? If so, what does the fan do now?
If the fan runs normally in above configuration, you could have either a RAM failure or a Hard Drive failure that is loading the bus of the Motherboard and causing problems. Download Memtest via Google and run a minimum of 8 passes on each stick of RAM individually. If Memtest returns any errors, replace each and every stick with errors with a new stick until Memtest passes on each and every stick individually with no errors. Next, is the hard drive. Download Seatools from seagate.com and run BOTH short and long tests. If any errors are returned, your drive has failed and needs to be replaced. Since most Toshiba Satellites use Toshiba drives, Seatools won't test this drive, you'll have to use other diagnostics such as WinDFT from HGST/WD here: http://www.hgst.com/support/downloads or ISO- linux GSmart Control. If the hard drive was replaced with a different brand such as Seagate *use Seatools as mentioned above* or Western Digital *use DLG*, you'll have to download and try those. Windows tools really don't do a good job with Toshiba's drives. That's where the ISO-linux tools come in. Just so you know, Toshiba hard drives have the highest failure rate of all laptop hard drives. So, chances are if it's keeping your fan from running properly, it's probably failed and needs to be replaced, regardless of what Windows diagnostics say. Linux diagnostics will give you a better idea; but even then it's not a 100% sure thing--and you may have to replace it.
If you have another working laptop hard drive around, you can plug it into your laptop in place of your existing drive and re-run above test. If the fan begins to run normally, that's pretty conclusive that your existing drive has failed and needs to be replaced. This is a very easy test compared to download all the above diagnostics and running them 1 at a time and trying to figure out how each works!
If the above test of removing RAM, hdd, and battery, makes no difference your fan is probably shot. Fans for Satellites are usually less than $10 on ebay. Since you've already got the laptop open, it's relatively easy to replace the fan; however Toshiba likes to put them in the most inaccessible place, so it's several hours to completely gut the laptop just to get to it. Replacing the fan should take care of your problem!
If the new fan fails to fix the problem, you probably have a bad fan control circuit and or sensor on the Motherboard and that's not a FRU. New Motherboard's run $80-$300 and up.
Let us know how it goes.