You mind icon in panel, or something else?
And there is:
Open Boinc manager
Snooze
About Boinc manager
exit
so no solution there.

But I want to see boinc manager. If I stop application then I can't restart manager, must first end process then restart manager. Bit awkward. I don't need that icon because I don't see any use.

Nop, can't start manager from terminal as root, can't start from menu.
yoss@gray:~$ sudo boinc
[sudo] password for yoss:
15-Apr-2019 10:47:51 [---] cc_config.xml not found - using defaults
15-Apr-2019 10:47:52 [---] Starting BOINC client version 7.9.3 for x86_64-pc-linux-gnu
15-Apr-2019 10:47:52 [---] log flags: file_xfer, sched_ops, task
15-Apr-2019 10:47:52 [---] Libraries: libcurl/7.58.0 OpenSSL/1.1.0g zlib/1.2.11 libidn2/2.0.4 libpsl/0.19.1 (+libidn2/2.0.4) nghttp2/1.30.0 librtmp/2.3
15-Apr-2019 10:47:52 [---] Data directory: /home/yoss
execv: No such file or directory
15-Apr-2019 10:47:52 [---] GPU detection failed. error code 512
15-Apr-2019 10:47:52 [---] No usable GPUs found
15-Apr-2019 10:47:52 [---] Creating new client state file
15-Apr-2019 10:47:52 [---] [libc detection] gathered: 2.27, Ubuntu GLIBC 2.27-3ubuntu1
15-Apr-2019 10:47:52 [---] Host name: gray
15-Apr-2019 10:47:52 [---] Processor: 2 GenuineIntel Intel(R) Pentium(R) CPU G3260 @ 3.30GHz [Family 6 Model 60 Stepping 3]
15-Apr-2019 10:47:52 [---] Processor features: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe syscall nx pdpe1gb rdtscp lm constant_tsc arch_perfmon pebs bts rep_good nopl xtopology nonstop_tsc cpuid aperfmperf pni pclmulqdq dtes64 monitor ds_cpl vmx est tm2 ssse3 sdbg cx16 xtpr pdcm pcid sse4_1 sse4_2 movbe popcnt tsc_deadline_timer xsave rdrand lahf_lm abm cpuid_fault invpcid_single pti ssbd ibrs ibpb stibp tpr_shadow vnmi flexpriority ept vpid fsgsbase tsc_adjust erms invpcid xsaveopt dtherm arat pln pts flush_l1d
15-Apr-2019 10:47:52 [---] OS: Linux LinuxMint: Linux Mint 19.1 Tessa [4.15.0-43-generic|libc 2.27 (Ubuntu GLIBC 2.27-3ubuntu1)]
15-Apr-2019 10:47:52 [---] Memory: 7.48 GB physical, 2.00 GB virtual
15-Apr-2019 10:47:52 [---] Disk: 400.61 GB total, 338.43 GB free
15-Apr-2019 10:47:52 [---] Local time is UTC +2 hours
15-Apr-2019 10:47:52 [---] VirtualBox version: 5.2.18_Ubuntur123745
15-Apr-2019 10:47:52 [---] Last benchmark was 18001 days 08:47:51 ago
15-Apr-2019 10:47:52 [---] No general preferences found - using defaults
15-Apr-2019 10:47:52 [---] Preferences:
15-Apr-2019 10:47:52 [---] max memory usage when active: 3827.57 MB
15-Apr-2019 10:47:52 [---] max memory usage when idle: 6889.63 MB
15-Apr-2019 10:47:52 [---] max disk usage: 338.33 GB
15-Apr-2019 10:47:52 [---] don't use GPU while active
15-Apr-2019 10:47:52 [---] suspend work if non-BOINC CPU load exceeds 25%
15-Apr-2019 10:47:52 [---] (to change preferences, visit a project web site or select Preferences in the Manager)
15-Apr-2019 10:47:52 [---] Setting up project and slot directories
dir_open: Could not open directory 'slots' from '/home/yoss'.
15-Apr-2019 10:47:52 [---] Checking active tasks
15-Apr-2019 10:47:52 [---] Setting up GUI RPC socket
15-Apr-2019 10:48:21 [---] GUI RPC bind to port 31416 failed: 98
15-Apr-2019 10:48:22 gstate.init() failed
Error Code: -180
Manager is running in background but can't be started as GUI

Two things from the above...

I thought 7.9.x was a test/develop/debug sequence for BOINC clients, production (or near-production!) releases have an even number after the first dot (e.g. 7.2.42, 7.6.31, 7.8.3, 7.14.2) -- I notice with some puzzlement that that seems to be the current Ubuntu 18.04 repository version for BOINC (so I'm glad I get mine - 7.14.2 - from the developer's PPA instead!)

If I assume you installed BOINC from a repository it should set it up to run the client at boot-time and it will probably have put the configuration stuff in /var/lib/boinc or /var/lib/boinc-client. You, however, are trying to start the BOINC client (not the manager) with the above command, and it's not doing very well as it can't find any of the control files in your home directory! (The manager is called boincmgr in my Ubuntu systems...)

(It's the second time I've seen someone trying this - the other was in the MilkyWay@Home forums!)

To find out if the client is already running do

ps -ef | grep boinc

and if there's a line like

boinc     1268     1  0 Apr04 ?        00:22:02 /usr/bin/boinc

that's the client running. In my case one of the other lines is

alanb     7714  5551  0 Apr04 ?        01:00:37 boincmgr

as I keep the Manager open on one of my (8) desktop views.

If the client isn't running, there's a fair chance that

sudo systemctl start boinc-client

will kick it back into life. (If MINT, like Ubuntu, uses systemd, anyway...) Once it is running properly, then debugging what's wrong with BOINC manager access should be a lot easier.

Sorry for possibly telling you stuff you already know, but (as you may have noticed from some of the replies you've already received) it's not always easy to help if one doesn't have a clear picture of the system being "debugged"...

Hope you manage to sort it out somehow.

Cheers - Al.