Hi Jesuspiece23,
Welcome to Sony Community!
The PCG-61611L is the chassis number of the laptop, the exact model name is usually located on the bezel of the monitor (VGN,VPC). If the laptop works fine without the battery inside but shows blank screen when you put it back then it looks like it has something to do with the battery.
Try to remove again the battery and use only the ac adapter. Turn on the unit and observe how long will it stays on. Now, put the battery back, check the health status of the battery by following the steps provided in the link below
https://us.en.kb.sony.com/app/answers/detail/a_id/43507/related/1. These steps will let you know if you need to replace the battery.
I hope this helps.
Regards,
Jen
If my post answers your question, please mark it as "Accept as Solution"