I was running anti-x with no problem on my laptop. I wanted to switch to Debian 9 and after installation, was given a "no operating system found" message. I figured it was a Debian issue and so, I tried Slackware 14 with ELILO. Same message.

I then switched my boot to UEFI Only and changed the boot order to Slackware -> USB HDD (my bootable iso). Now, It begins to boot, but I get stuck at an "end trace" message. Can anyone help me? I just want to have a working distro on my laptop; preferably Debian.

Sounds like when the Debian installer asked you where you wanted the grub boot loader that you chose the drive partition & not the MBR.

(I don't do UEFI, so it may be different for that. )

I notice you say USB drive - likely it has the wrong drive designation in /etc/fstab - it needs to be the first drive to boot - i.e. /dev/sda, not /dev/sdb which is possibly what you have.

Personally, I've had extreme difficulties installing Linux on a ThinkPad. I have an older IBM ThinkPad which doesn't support PAE. I tried installing Linux Mint, which is a non-PAE distro; then I couldn't get it to dual-boot with Windows XP. Grub would either boot XP, or Linux Mint, not both. So I see that your ThinkPad is a Lenovo, so I imagine it's newer, but I'm wondering if PAE could still be an issue?

At any rate, an easy test would be to create a Live USB or Live CD of Debian 9 and trying it out to see if it's compatible with your computer.

I have TWO i3-3227u based x131e Lenovo Thinkpads, purchased used from eBay, the first one for ~$175 about a year ago, the second for $109 about a month ago. I replaced the mechanical HDDs with 240GB HP SSDs, and maxed out the RAM to 8GB. I installed Win7SP1, then MX17.1, then AntiX 17.1 (using an Easy2boot formatted USB3 stick), in a triple boot configuration: ~175GB NTFS partition, ~3GB Swap partition, ~39GB BTRFS for MX, ~23GB EXT4 for AntiX. MX seems to run better with BTRFS for some reason on Thinkpads, at least for me. And I DON'T encrypt my home folders during installation--my data ain't that valuable! I set both up to use the AntiX Grub menu installed on the default MBR, though MX's Grub also works--AntiX is just "prettier".
I haven't had ANY problems. ALL x86 capable cpus manufactured since approximately 2005 have been PAE-capable, including the 1st generation 32bit only Atoms, so PAE incompatibility shouldn't be a problem. Since AntiX 17.1 (and MX for that matter) is based on Debian 9, I'm kinda fuzzy as to why you'd want to ditch AntiX for 9 in the first place. The easiest solution would be to reformat your internal HDD and do a fresh install of your chosen distro(s).