How you worded
I have tried to copy a folder from my C drive to the SSD drive.
suggests that your C:\ drive is a hard drive and your G:\ drive is your Samsung 830 SSD.
35,575 files that only take up 504 MB could be fragmented on your hard drive, which easily makes your hard drive the bottleneck.
Assuming that each file is contiguously 14.167 KB (504 MB / 35,575 files), but all the files are at different physical locations on the hard drive, one file takes about 10 ms to transfer (9 ms seek time, 1 ms read time). You can transfer 100 files in 1 second, and at 14.167 KB per file, that's 1.417 MB/s.
But that's a guess on the extreme end. Some files may be larger or much larger than other files, and since they're likely contiguous for the most part, there would not be seek latency on the hard drive. Some small files may also be sequential (not sure how NTFS handles sequential small files being transferred, though).
The solid state drive should be much faster than the hard drive, so it should minimally affect how fast the transfer is. (The hard drive is maxed out.)
My point is that your screenshot showing 3.34 MB/s makes sense when copying your sort of data from a hard drive to a solid state drive.