I have an old HTC Sense and i am having problems getting market to open or even updating to google play store. I have an old HTC Sense Android, running 2.3.4, I'm not new to this scene, i currently have a galaxy S6 Active and a S8+, but im still learning, ANYWAY this phone doesnt have service, just wifi, i was bored and It has market, but won't connect. Did they make updates to install google play store, ?? Does the Android market even still exist..?? I appreciate any help.       - D.W.O 
I have just seen that in settings it says 2.3.4 but somewhere else i saw 2.3.6...also this device is stock, i have no clue about rooting...would like to learn
"Android Market" has been renamed to "Google Play Store" long ago. Afraid Google also changed the API since and deprecated the old one, so you won't be able to use this "ancient" version anymore.

For an alternative, you could try F-Droid, an open source Android "market" which should still work with "ancient versions". There you'd also find apps like Yalp Store, which would allow you accessing Play Store.