Re: Slider mechanism broken?
There is a fix. Your slide flex cable is to be replaced. It is a flat flexible cable which maintains the connection between the two screen/trackpad/keys and the main unit with the keyboard/motherboard/camera when they are slid apart. It is not that easy of a fix to do yourself because to get to the flex cable you have to unstick the touch screen off of the lcd then unscrew the final 2 screws to free the slide mechanism from the back of the lcd. Then you will have access to the flex cable. A flex cable off eBay or Amazon goes for about $20. If your phone is on contract and still has a warranty you will probably get a new unit or even a free fix. If it isn't and you or an unauthorized repair place tries to fix it that will void any warranty because of breaking a seal that exists on one of the screws next to the SIM card.
If you are going to do it yourself:
1) Find videos on youtube about replacing 9810 housing, 9810 disassembly, or switching housing to white from black. They have good step by step one by a British dude. (9800/9810 have almost identical build so looking at a 9800 disassembly video won't hurt because there are more about the 9800 than 9810).
2) Get the required tools (T2,T4,T6, pry tool, needle nose pliers, double sided 2mm tape/ digitizer tape replacement, moist monitor wipes, and a new flex cable etc.).
3) Slowly take it apart following a good video and replace the flex cable on the slide mechanism (It's not too hard because you see exactly how the old one was on there).
4) Most important step, when putting the digitizer back onto the lcd remember to wipe clean the inside of the digitizer and the lcd checking under different angles for dust/fingerprints. If the glue on the digitizer has any discontinuity you must add a piece of tape to make a seal/replace the whole glue area in order to prevent dust from coming in after the unit is reassembled. You don't want to have a big fingerprint on the inside of the glass or pieces of dust staring you in the face after all that hard work. So if you have a replacement digitizer tape then use it after peeling away the leftover original glue.
Or- pay someone to do it...