Zinnias are one of the easiest seeds to plant directly in the garden. If you dont have lights for them inside then I would suggest that you just start again, outside.You might want to take a look at the post half way down this forum "windowsill/shoplight comparison"

Leggy over crowded seedling are unlikely to recover well. That said - if you cant just abandon your babies, try transplanting. If its warm enough I'd put them directly in the ground, but shade them for the first week to protect them.

THank you Mandolls for your reply. How warm is warm enough? I wander if I should still wait.
I am definitely going to try transplanting but I will probably get another set directly in the garden. Thank you for the advice!

I am also wondering if I will have the same problem with my Petunia seedlings, they are very crowded as well.

By warm enough I mean no more frosts likely. Though if you are obsessive compulsive enough you could put little plastic cups over them if you get a frost warning. I am in zone 4 where the last frost date is officially March 31st. I usually push it to mid March and keep my fingers crossed, but its definitely to early right now for me to put out anything that isn't frost tolerant. You could also keep them in pots for a while, and take them outside during the day, bring them in at night, but that wont help the over crowding. Search "hardening off" on this thread before you move them outside, so that you understand that they need a gentle transition. - Petunias will have the same issues, but they are much slower growers than zinnia, & need more babying, I am trying them for the first time this year myself, so cant give you any solid advice.