How to exit grub rescue?
Solution 1:
To leave from Grub's rescue mode and reboot the machine simply type
reboot
and hit Enter
Before doing that you should insert your live-USB or DVD. When the machine reboots, enter the BIOS/UEFI-settings to change the boot-order accordingly to boot from your live-USB or DVD.
It is hard to say what your problem really is, deleting the swap-partition usually doesn't result in a boot-failure, it will increase boot-time (at least this is my experience and may depend on the version of Ubuntu you use).
So you should add more information to your question. When booted into Ubuntu-live, open Nautilus (Files) and mount your Ubuntu-partition on your HDD/SSD with a left-click on it. You should see the file-system on your partition now. Browse to find the file /etc/fstab in this partition, open the file with a double-click, copy the content and paste it into your question.
Then open a terminal and run the command
lsblk -o +UUID
Copy the output and paste it into your question as well.
This will help us to determine what is going on.