Hi Yaniz,
1 Try removing the battery and the power supply wire....(make sure the computer is fully powered down...not just a sleep etc)
2 Next connect the power wire (but leave the battery disconnected)
3 Try to power on your computer...does it start OK?
Report back with what happens at step 3
If it doesn't start then its likely a power issue with the external power supply unit, power wire, motherboard socket/connection, or mains electrical outlet.
These are the things you need to check:
3 Check power (voltage) at the electrical outlet is correct for the location you are in (In my country, for example, it should be 230v (plus or minus 5%) in US of A it is probably around 110-115v and other parts of the world may have different "national" voltages.
4 check the output voltage at the end of the power wire (where it plugs into the computer) for this Toshiba it should be 19v
5 If you have access to a known good working power supply of the correct rating then it would be worth trying that and see if it helps
Please don't take any risks when trying to check things out, if you are not absolutely sure of the correct and safe way to do it the get an electrician or competent computer technician to do this for you.
Post back and let us know how you get on.
Regards
paws