There are various ways around this, but what I would suggest doing is cloning the system partition of your 250Gb drive to the newer 350Gb drive.
Then once you are able to safely boot off the 350Gb alone, re-connect the 250Gb hard drive & backup the other partition (if required) to the 350Gb drive by simply copying + pasting.
The above steps takes care of backing-up both the 250Gb drive's partitions & the entire drive as a whole.
Next, go into Disk Management & delete both partitions on the 250Gb drive. Then create a single large partition & format it.
Now you're left with 2 drives, both having a single large partition. I'll be back to suggest a suitable cloning program.... G