Difficulty engaging third gear is a fairly common fault on pre-1999 models, this is typically the first gear to go bust (for reasons unknown). Gearbox synchro seems the most likely suspect for the third-gear issue, but doesn't explain the original comment about not getting into ANY gear.
If the car goes into gear when cold, but not once heated up, I personally think the problem might lie with the clutch as opposed to the gearbox linkage. I *think* the pre 2000 Ka uses a hydraulic clutch, so leakage of fluid is the most likely culprit, followed closely by an air bubble in the system. I’m still not happy with this as an explanation (it doesn't really explain why you can change when the car's cold but not when it's warm), but checking the hydraulic fluid levels is a good place to start your fault-finding.
If it's not to do with the fluid (or a stretched cable if your car uses a cable system), a replacement clutch kit might be the solution. The parts aren't OTT price-wise (maybe about £75), but as per usual it's the labour that'll run away with your cash. There are also companies that will come out and perform clutch repairs at your house as opposed to taking the car to a garage - this type of repair will cost less, assuming it's possible to fix the clutch without lifting the engine (depends if the clutch can be accessed in-situ). However to do this, you'd first need the problem identified definitively, otherwise you’re wasting time and money.
New gearboxes aren't that expensive or hard to find either - I believe they are shared with the fiesta mk4 - however there isn't really enough value in older, higher mileage Ka's to justify a full replacement of the gearbox, especially considering labour costs if you're taking it to a garage. Depends on the trim level, mileage and condition - what are you going to get if you sell it fully working? Is it going to be worth £200-£300 to repair a knackered gearbox?
One further problem which I've head about a few times is a rattling noise when the clutch is depressed - this is most likely a worn thrust bearing - however you'll be pleased to hear that, although inconvenient, this is far from fatal and normal driving can be continued for months - mechanics might tell you that a new clutch is required immediately, however provided you're not taking the car round race tracks, you may as well get every last mile out the existing clutch (once it starts crunching gears and causing further damage, then you can think about replacing it). When my clutch started doing this, I took it to the garage, where the mechanic told me I needed “a new clutch straight away” - two years later I've still got the same clutch, and that's with urban driving during the week (i.e. constant gear changes) and 100-mile motorway trips (i.e. staying in gear for a prolonged time at high load) at the weekends. Seriously, I've done about 20,000 miles since the guy said the clutch was on its last legs, and the problem hasn’t significantly worsened.
Please bear in mind that although I'm a bit mechanically-minded, I'm far from a qualified mechanic. Much of the above is opinion, research and learning from previous disasters, but I hope it’s helped in some way.
Ka-rma Sutra, January 2009