My experience with Toshiba laptops is that the power supply is the weak point. The battery stops recharging and then the power supply start playing up. When you switch it on, it just goes pop and then you can't switch it back on. Luckily I did not have these problem until after about 3 years.
Because the laptop is out of warranty, you have to prove that there is a manuafacturing defect. If you have proof that there is a defect, you may be able to get Toshiba to pay for the repair.
So your next step is to take the laptop to be inspected and for a technician to provide their opinion as to what the problem is, plus the cost to repair. You can look locally for laptop repair specialists, PC world used to offer a fixed price service or contact the Toshiba customer service line as they may take a look at it for you. Probably contacting Toshiba in the first instances may be the best option as they probably have a process for this.