After the file system warning me about low disk space, when I try to log in it's showing me the message on the screen dev/sda clean XXXXXX/XXXXX files XXXXX/XXXXX blocks hence I cannot access my GUI.
The problem is not related with graphics or anything, it's just a low disk space problem. Do you recommend Gparted with LIVE USB to extend the partition? If so show me the steps.
Before you try partitioning operations, first check what the problem really is.
That message "/dev/sda clean XXXXXX/XXXXX files XXXXX/XXXXX blocks" is the output of fsck, and it's actually good news: It tells you that the filesystem check did not find any problems.
You wrote that you got a "low disk space" warning. Was that while software packages were being upgraded, i.e. the normal system update?
Did you get a chance to check your disk space to see what was going on? It might be a runaway log file, it might be files that you created in your home directory, it might be anything.
First, find out where that disk space went, and if you really need to resize partitions. What size are your Ubuntu partitions? Do you have a separate partition for /home? Are you using LVM and/or full disk encryption?
I recommend you get a Ubuntu live system on a USB stick, boot from that and mount the root filesystem from your Ubuntu disk and first have a look. Follow the link provided by @guiverc for the first steps to boot and mount the partitions.
Then please edit your question to include the output of
lsblksudo parted -lfindmntdfeach one formatted as code, please, i.e. with a line consisting of three backticks ``` before and after.
If it turns out that your root filesystem is really nearly full, we can continue to give you more hints.
