Carriage remains stationary when typing. Is there a way to unlock

I've seen one on an olympia typewriter. Like a switch on the left side of the machine next to the numbers line. Your problems could be Lock is bent, not connected fully, needs cleaning, oiling.
http://www.ebay.com/gds/How-to-Fix-a-Royal-Typewriter-/10000000205719319/g.html
This link may help. Some of the fix-it advice. Pay attention to carriage won't move paragraph. Check library for possible owner manuals, repair manuals.
Just found this link that may offer more help.

http://www.vintagetypewritershoppe.com/vintage_typewriters_22.html

Christine: According to VintageTypewritterShoppe.com: "Underwood portables have a simple carriage catch on the left side right below the carriage. Move the carriage to the right a few inches to disengage. Remington portables have two systems. Early portables require the sliding out of the platen shaft/knob on the right end of the carriage. The lock lever is located on the left end of the carriage and is spooned against the left side carriage release lever. Newer Remington's(Model 5/Streamliner/Deluxe) have a small lever on the left end of the carriage located in the same spot as the earlier models. There is a little ball on top of the lever. Push the lever to the rear to disengage the lock."

most portable typewriters have a center lock mechanism usually under the carriage front it could be either on the left or right side

Belt is slipping or broken..When it sits for awhile the belt stretches.

Usually when this happens part of the case or carriage is loose or bent. Move it back and forth and try to see what it is dragging on.

DICKYO

Make sure the carriage lock switch isn't on (presuming it has one). A carriage lock switch prevents the carriage moving when in transit (say, inside its case). These switches are usually located on the right hand side of the carriage, slightly underneath.
Gordon

Many of these older portables have a carriage lock, usually just below the carriage on the L. or R.

DickyO

Learn how to unlock the carriage in Olivetti Lettera 22 Manual posted by Ed Cornish (Carriage Locking Lever 7). It is a different machine model, but the lock/unlock mechanism might be the same.
You can see the full manual at Ed’s Flickr account or you can download it from here: http://dl.getdropbox.com/u/1322442/Olivetti%20Lettera%2022%20Manual.pdf (temporary link)

YEP, MOVE THE PAPER FEED SELECTOR TO NUMBER 1

The solution is not right--there is a carriage return release lever on the far right of the typewriter, that engages a notch on the underside of the roller/carriage return--push it forward to release the lever and you are in business--it has a spoon shaped end and its on the right side