Can I backup bricked Xperia X?

my trusty xperia x died without a warning and i want to somehow access the files in it. i managed to turn the blue led on while connecting to the pc but nothing else seems to work

I know you asked for help with backing up, but have you checked out for any pointers?, maybe you can restart your device?

You should be able to pull the partition something like this:

Then you of course need to mount that. So if you are not on Linux you are probably in for a bumpy ride.
I haven’t done this end-to-end myself, so no possibility to provide more details… but should be fairly googlable.

Did you check @Edz’ answer?
You need to follow another link on above linked page to get to the site for the X.
Without telnet access this might not work:

In that case you may try the Android way to get access to the 51 partition!
But: do NOT flash TWRP (as suggested in @attah’s link) or any other recovery yet, just try to boot it.
Another good read may be this (not directly related to your specific problem but has some basic details!):

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how can i boot anything? the screen does not turn on at all

i’m worried i’ll lose all the data if i try to reset the device

You really need to read through the contents of the link. There are given methods of recovering data. Obviously if the given methods don’t work, you will need to lose the data in order to get the device running again, or leave it as a brick.

i don’t plan on using it again, i’m done with sailfish it has become unusable ever since 4.0
i just read through the link and i cant do it since i don’t have an sd card, also its on the first version 4 so theres no way to get hybris-recovery.img version of it

So you did not start at all?

Grab any recovery.img (4.x) you can get. As long as you only read it should not harm.

Then at least get the device into fastboot mode?
(vol-up and plugin USB)
and then read/continue with zendesk link…

A SD card just makes sense (is not that expensive at all and should be at hand) else you might use netcat (nc) and / or basic /dev/tcp stuff, e.g.
How to open a TCP/UDP socket in a bash shell