My internal memory is 1 GB. After I reboot it changes to 64 MB. When I check the space on internal storage, I only see built in apps and shows no free space.
No, there is no way to increase internal memory; this is installed at the factory and is fixed. You can, however, free up existing space on your internal memory by removing apps, cleaning out caches and deleting end user files that are stored there. Modifying stock apps (ie, removing bloatware) usually requires a rooted device, and will prevent you from receiving over the air updates as well as most likely voiding your warranty.
Look under Settings / Applications / Memory then narrow down to "running", and see what is taking room.
Before I found "running", I noticed that NFS Shift and Let's Golf took a very large amount of "memory" (akin to disk space) so uninstalled them.
Then under Running, I could see if there were any things running that I didn't want, in my case skype was running (I use the chat), IMO was running (I use the chat), etc. but if I'd have found things I didn't want running I would see what I could do with them.