Contour Flexihead, I have a loose connection around about the cable entry. How do I open it. 3 Svrews removed but nothing comes apart

Try 'tightening' the screws first even if just a bit. This can possibly break them loose so you can remove them with the normal counter-clockwise motion.

If the vacuum runs well with no other problems it may be worth buying a new cord reel. It may be less expensive to purchase a new vacuum but it may not last as long as an older machine. I have many 10 to 20 year old vacuums brought into my store for routine maintenance. Do not try to replace the cord as you are correct, the spring come flying out.

THE PRODUCT HAD TO GO TOGETHER...SO IT HAS TO COME APART!! KEEP LOOKING FOR MORE SCREWS..OR A LATCH TYPE SET UP. ONCE INSIDE, SECURE ALL LOOSE WIRING TO CONTACT SCREWS...OR? MAKE SUR PLASTIC CORD RETAINING COLLAR IS AROUND CORD, AND FASTENED PROPERLY TO VACUUM OUTER HOUSING!
** NEXT....VACUUM THE CARPET!

Even with your explanation,it seems the hose is clogged.Try taking the hose off,then blow through it or pour water through it.If this doesn't do it,make sure the suction canals are going to the proper areas.

I have the same problem with my older '80s Tristar.
This may work for your model, give it a try.
On mine, there are 3 phillips head screws holding the two halves of the cleaner together, and the rubber bumper.
You have to remove the screws first. Your model may have more or less screws.
On mine, there are two screws near the front wheels, down deep. I had problems taking them out, but not to worry, once they are loose, they are no longer holding the other half, don't worry about taking them fully out.
Also, at the rear, there is a small black plastic clip that has a screw in it. You'll need to remove that too. Once all the screws are removed, use a medium sized flat head screwdriver to go behind the rubber seal -- you're looking to get the screwdriver to where you can see or feel the edge of the canister. Simply twist the screwdriver a bit and the canister should feel like it's coming apart. Mess around with that for a bit, and the parts should come apart easily.

I have listed below a link to the owners manual for your model and a link where you can purchase the belt you need. Hope it helps you!

Eureka Contour 2900 Owner's Guide

Eureka Contour 2900 Belt

hi may i suggest ? if you wish to renew the complete cord/wire? why not fit a longer length to facilitate more reach thro different rooms from the preferred wall socket ? the problem of short /breakage of wires within outer sleeve near casing is common on lots of vacs it is not a difficult job to replace if you are competant with wire and colour codes remove the access cover where wire enters vac then observe the attachment of each wire ? then disconnect faulty cable transfer the rubber tube that is normally fitted at entry point to vac at this point to new cable remove outer sleeve of new cable same length as old cable to reveal the inner wires then connect to vac sockets resecure cable to vac as previous dont forget the rubber tube? refit entry cover and fit a new 3 pin plug bs kite marked ? then away to vac the rooms? hope this helps

Take off the strip that runs around it, then you can get to the casing clips, remove them and the 2 halves come apart.

Remove the belt or seal that goes around it, there are some clips to take out, then it will separate.

You need to unscrew the screw at the back / base of the handle. The whole handle section will need to be slid backwards. Best way is to unscrew the screw on the rear approx 5 turns and then bump the end of the screwdriver. A few more turns then bump the end of the screwdriver again. The whole handle will eventually slide backwards and fall off. Then unscrew the two screws at the front (near switch) and the front switch cover plate will lift up (hinging at the top). This reveals the incoming wires etc.