Just started having this problem three hours ago. My laptop's battery died and shut off while I was working. I plugged the charger in and turned it back on (wasn't planning on continuing to use it while it was charging, I'm really paranoid with leaving my laptop off for a long time because I feel like it won't start ever again) Anyway, I turn it on, I get the Toshiba Leading Yadda Yadda screen without the white spinning cursor dots then with the cursor dots but then after a while of that, the Toshiba logo disappears but the cursors stays there and it just keeps spinning. The screen is black or rather dark grey but the cursor is still there. It's not the Windows spinning cursor, it's the Toshiba spinning cursor. Don't know what to do now. I have a Toshiba Satellite C55-B5362 Intel Inside Core i3.
Could you check if it is possible to open the BIOS menu at startup? If it is not possible, there may be hardware issue with the PC. Disconnect battery and remove the power cable. Hold the power button for 20 seconds and reconnect the power cable. Try to boot again. Is the laptop under warranty? If it is, I would recommend you to contact the seller and ask for guidance.
If you have a Windows installation drive, try to boot from it. If it is possible, select the Repair option. It may fix booting errors without harming your data.