I recently upgrade the ROS of my RB433 to V6.36, Using Winbox. As indicated in the how-to guide, I issued the "/system routerboard upgrade" command in a terminal window and then clicked System -> Reboot to complete the upgrade. The device did not reboot, but rather froze, with four LEDs (LD501 to LD504) lit up. I left it for a good 15 minutes but nothing happened.

I cycled to power to the RB and used the ROS Reset switch (shorting the contacts) to reset the RB to defaults and then it did boot up. Winbox indicated that ROS V 6.36 was running on the RB, but when I issued the reboot command it froze up in the same way again. It also seems to freeze up if I cycle to power to the RB to quickly - I need to power it off, leave it off for say 20 seconds and only then will it boot up.

I then used NetInstall to load ROS V6.36 - After the ROS file transfer was complete issuing the reboot command from the NetInstall GUI gave the same result
I then used NetInstall to load ROS V5.26 - This also gave the same result.
The RB does not seem capable of following a Reboot command.

Is there something wrong with the RB? Did I perhaps miss a step or do something out of sequence?

Try this
/system routerboard settings set force-backup-booter=yes
then reboot.

Thanks for the suggestion. It didn't fix the issue though.

While I was tinkering with it tonight it seemed to freeze up once or twice in the same way without me even issuing the reboot command.

I'm beginning to suspect the rb is damaged somewhere...

 Do any of the capacitors appear swollen or leaking?
Been the cause of many a headache with older routerboards.

There is a cluster of three green caps that appear to be buldging ever so slightly - ie they aren't 100% flat on the top like the other black caps. There is also a bit of orange residue on the top of two of the green caps.
If memory serves me correctly I bought this RB in 2010.
So that is probably it.

Some pictures here:
https://drive.google.com/folderview?id= ... GVlMEl1TDg

I looked at the bottom of the board and it doesn't seem like they'll be that hard to replace.
The spec on the side of all three caps is 560uF - 6,3V. Anything else i.t.o. the spec of the caps I should know, or can I just buy any generic caps with the capacitance, voltage rating and package size? (sorry for asking, but I last played with electronics about 10 years ago)

I noticed there are quite a few discussions around faulty caps already. Even searching for "560uF 6,3V capacitor" on Google, returned the MikroTik forums as the 5th result.

Will do a bit of reading, but any advice on what caps to use as replacements would be welcomed.

Just swap the capacitors by the new with the same parameters. If rated by higher temperature, or a bit higher voltage - only better.

Thanks for the advice - will swap the caps and post here if it solved the problem.

Update: Swapped out the old Su'scon 560uF 6.3V caps with new Rubycon 560uF 35V caps. 
The package size is quite a bit taller but only 2mm wider so they fit ok onto the circuit board. Luckily I have a deep enclosure that houses the RB, so the extra tall caps aren't a problem.

Now the RB433 operates as expected -> boots up properly, reboots on command, etc. etc.

Thank you for the advice Aug and Jarda!

Good job. Such capacitors will survive the rest of the board for sure.