Before I give up I might as well inquire here too.  I have an old IBM PC hard disk controller that only works when it's cold.  It's an IBM 1501492 (Variation 1).  I found if I start up a read test then apply freeze spray within the red rectangle, the drive begins recording successes for several seconds.  But I can't narrow it down any further.  Two precision sprays with no visible overlap in visible frost can both be effective, and how effective a spray in a given spot seems random.  Sometimes a spray in one location results in 5 seconds of successful reads, then another spot give me 20 seconds.  Then I'll repeat and get roughly the opposite result.  So I'm not able to pinpoint a specific component.  Any ideas before I toss it?  I suppose I could guess and re-solder random stuff in that region, but I'm lousy at soldering and it may or may not be a solder joint failure.

Clearly a broken connection somewhere, but it could be a solder joint (or the in-hole coating or a via through the board), but as well something within some component.
Try to carefuly spray just on a single component, one at a time. Just really small dips of the cooling liquid onto the component under test.
Then from the bottom on the board itself.
Or try to identify the components (what is a transistor, its type,...), then do basic in circuit check on them once the board starts acting up - which transistor junction changes its drop,...

As a last resort you may try to resolder all components on that area, but better on both sides of the board, as the crack could be within some of the plated holes.

Wow Patrick Still using the old IBM PC XT?  I still have one that the last time I used in the late 1980s.  I found the hard drive and its controller from some kind of used computer warehouse for USD $55 and added to the IBM PC XT that I found from the community college electronic department when I was attending.

Ah, memories..! The first (IBM) computer I ever used was when I worked for British Rail in the 80's, it was a 3270 PC, which was basically an XT with lots of extra bits bolted on to allow it to do dual duty as both a standalone PC and an IBM mainframe terminal. It was quite good to use, actually, it had a colour screen (rare back then) and a humongous 122-key keyboard, with more function keys than letters of the alphabet 

I did briefly have a standard XT at home, but it was used mainly as a monitoring device for the amateur radio packet network, and didn't really see any serious keyboard-bashing. Main machines at that time were 386's and 486's.

I hadn't powered my IBM XT on in about 10 years.  When I finally did a couple months ago, it emitted a loud squeal followed by a pop and foul odor.  One of tantalum capacitors on the hard disk controller had shorted (doesn't seem related to the current issue), and the power supply failed (perhaps the shorted cap took the PSU down with it).  For now I have a compact AT-type power supply installed, but it doesn't fit properly so I'd like to get a genuine XT power supply at some point.  Perhaps the old one can be repaired.  Right now all it does is produce a ticking/clicking sound.

The old PSU probably just needs capacitors to be replaced...

I hadn't powered my IBM XT on in about 10 years.  When I finally did a couple months ago, it emitted a loud squeal followed by a pop and foul odor.  One of tantalum capacitors on the hard disk controller had shorted (doesn't seem related to the current issue), and the power supply failed (perhaps the shorted cap took the PSU down with it).  For now I have a compact AT-type power supply installed, but it doesn't fit properly so I'd like to get a genuine XT power supply at some point.  Perhaps the old one can be repaired.  Right now all it does is produce a ticking/clicking sound.

Hi,
tantalium capacitors often fails short, so i think it had done some damage to your power (try to check power section like diodes, capacitors, drive transistors/mosfet and, of course, the transformer).
As told by Medved, check solder joints and try to resolder components, also try to chec components when board is not cold: myabe one of them had degraded with age.