My Canon 600D was working fine till the last two months when issues started rising. When I switch it on, I don't see the red blinking light and it's not turning on. The last time, I removed the battery and memory card, and after some time it worked fine. What might be the possible reason for this malfunction? And how much will it cost to fix this?
I haven't tested it with a different battery, and I used a micro SD-to-SD adapter but the camera got super hot, and the memory card adapter got hot as hell.
If I were you, I'd go ahead and buy another battery on Amazon. If a new battery fixes it, dispose of your old one, and you're good for $15. If not, it might be an internal problem and you'd probably have to send it to Canon.
Edit Per OP's comment, the problem seems to have been narrowed down to whether the memory card is inserted or not.
Try it with a new memory card. Something reliable, like a Sandisk. Again, if that doesn't fix your problem, you might have to send it to Canon for servicing. Prices can vary, so a quick phone call to Canon's customer service (1 (800) 652-2666) would be the most reliable source.
I have the same problem with my 600D. I don't know what does this issue depend on, but nowadays my camera does not turn on. Sometimes it happened before, but nowadays it does not work. Only after trying a lot of removing the card, the lens and the battery helped; but the last time when it has turned on I opened the card slot and the device immediately stopped working. I closed the card slot and it did not started to work. Turned it off, turned it on; removed the battery and still nothing happened. After that I noticed a strange clack coming from the inside of it, then I removed the battery again; the noise just disappeared and did not come back anymore. I tried 5 different batteries and three different memory cards, the camera neither does work with them. Any ideas about this...? :/