Hello!
Not managed to find similar question or something useful with help of Google... I have two Ethereum nodes running based on Parity:
Here's the first one:
resurtm@resurtm-thinkpad:~$ screenfetch
./+o+- resurtm@resurtm-thinkpad
yyyyy- -yyyyyy+ OS: Ubuntu 16.04 xenial
://+//////-yyyyyyo Kernel: x86_64 Linux 4.4.0-47-generic
.++ .:/++++++/-.+sss/` Uptime: 1d 1h 17m
.:++o: /++++++++/:--:/- Packages: 1600
o:+o+:++.`..```.-/oo+++++/ Shell: bash 4.3.46
.:+o:+o/. `+sssoo+/ CPU: Intel Core2 Duo CPU T7500 @ 2.201GHz
.++/+:+oo+o:` /sssooo. RAM: 1572MiB / 7910MiB
/+++//+:`oo+o /::--:.
\+/+o+++`o++o ++////.
.++.o+++oo+:` /dddhhh.
.+.o+oo:. `oddhhhh+
\+.++o+o``-````.:ohdhhhhh+
`:o+++ `ohhhhhhhhyo++os:
.o:`.syhhhhhhh/.oo++o`
/osyyyyyyo++ooo+++/
````` +oo+++o\:
`oo++.
resurtm@resurtm-thinkpad:~$ dpkg -l | grep parity
ii parity 1.4.4 amd64 Ethereum network client by Ethcore
resurtm@resurtm-thinkpad:~$ apt show parity
Package: parity
Version: 1.4.4
Status: install ok installed
Priority: extra
Section: science
Source: parity
Maintainer: Ethcore <[email protected]>
Installed-Size: unknown
Homepage: https://ethcore.io
Build-Depends: debhelper (>=9)
Standards-Version: 3.9.5
Vcs-Git: git://github.com/ethcore/parity.git
Vcs-Browser: https://github.com/ethcore/parity
Download-Size: unknown
APT-Manual-Installed: yes
APT-Sources: /var/lib/dpkg/status
Description: Ethereum network client by Ethcore
Syncing stalled at this state:
http://i.imgur.com/92ThVXj.png

And here's my second node:
resurtm@resurtm-desktop:~$ screenfetch
_,met$$$$$gg. resurtm@resurtm-desktop
,g$$$$$$$$$$$$$$$P. OS: Debian testing stretch
,g$$P"" """Y$$.". Kernel: x86_64 Linux 4.8.0-1-amd64
,$$P' `$$$. Uptime: 29m
',$$P ,ggs. `$$b: Packages: 1704
`d$$' ,$P"' . $$$ Shell: bash 4.4.0
$$P d$' , $$P Resolution: 1920x1200
$$: $$. - ,d$$' DE: XFCE
$$\; Y$b._ _,d$P' WM: Xfwm4
Y$$. `.`"Y$$$$P"' WM Theme: Default
`$$b "-.__ GTK Theme: Adwaita [GTK2]
`Y$$ Icon Theme: Tango
`Y$$. Font: Sans 10
`$$b. CPU: Intel Core i5 CPU 760 @ 2.801GHz
`Y$$b. GPU: GeForce GT 640/PCIe/SSE2
`"Y$b._ RAM: 3455MiB / 16041MiB
`""""
resurtm@resurtm-desktop:~$ dpkg -l | grep parity
ii parity 1.4.4 amd64 Ethereum network client by Ethcore
resurtm@resurtm-desktop:~$ apt show parity
Package: parity
Version: 1.4.4
Status: install ok installed
Priority: extra
Section: science
Source: parity
Maintainer: Ethcore <[email protected]>
Installed-Size: unknown
Homepage: https://ethcore.io
Build-Depends: debhelper (>=9)
Standards-Version: 3.9.5
Vcs-Git: git://github.com/ethcore/parity.git
Vcs-Browser: https://github.com/ethcore/parity
Download-Size: unknown
APT-Manual-Installed: yes
APT-Sources: /var/lib/dpkg/status
Description: Ethereum network client by Ethcore
So far so good on this node:
http://i.imgur.com/TjadT2x.png

The question is: what can I do to solve the stall issue at my first box? Parity is latest for the moment, cannot imagine what causes that.
I appreciate any help! ;-)
Thanks!
It seems that your node is not stalled, it's just taking a lot of time to process those blocks.
Notice that the number is increasing (although it takes around a minute to process the block), also the green number 15591 indicates that there are 15k blocks already downloaded and waiting to be processed.
If you have HDD drive you may consider resyncing with --db-compaction hdd, also you may try --warp sync to get the latest state in ~15minutes
@tomusdrw, thank you for quick reply!
Trying both options...
Launched with both options, this is what I've got:

I know it's not stalled, and is working, but with such speed it will take forever. Current block is #2427971, total block count is #2690764 (https://etherscan.io/txs), at the moment of writing this. I'll leave my PC to work a bit, maybe it will become faster... :-(
Those are most probably the blocks when state bloat attack was ongoing, they take quite a while to process on HDD.
So if you wish to use --warp sync it might be better to actually remove blockchain data and re-sync with --warp from scratch. For default location and mainnet:
# Remove the chain
$ rm -rf ~/.parity/906a34e69aec8c0d
# Start Parity
$ parity -db-compaction hdd --warp
@tomusdrw, thanks for help!
Thank you for your help! ;-) I'm finally now with the latest block. Nice!
Parity is just a fresh air comparing with go-ethereum. Took only 24 hours to manage to sync all blockchain. With go-ethereum I was having issues for about 2.5 weeks.